Answer:
a. E = 86.36 x 10⁻³ V/m = 86.36 mV/m
b. ρ = 3.6 x 10⁻⁷ Ωm
Explanation:
a.
The electric field in terms of the voltage is given by the following formula:
E = V/d
where,
E = Electric Field in the Wire = ?
V = Potential Difference = 3.8 V
d = distance between the points = 44 m
Therefore,
E = 3.8 V/44 m
E = 86.36 x 10⁻³ V/m = 86.36 mV/m
b.
Now, from Ohm's Law:
V = IR
R = V/I
where,
R = Resistance of wire = ?
I = Current = 3 A
Therefore,
R = 3.8 V/3 A
R = 1.27 Ω
Now, the resistance of a wire can be given as:
R = ρL/A
where,
ρ = resistivity of material = ?
L = Length = 44 m
A = Cross-sectional area = πr² = π(0.002 m)² = 1.25 x 10⁻⁵ m²
Therefore,
1.27 Ω = ρ*44 m/1.25 x 10⁻⁵ m²
(1.27 Ω)(1.25 x 10⁻⁵ m²)/44 m = ρ
ρ = 3.6 x 10⁻⁷ Ωm
Which of the following describes the motion or change caused by a transformation from electrical to sound energy? (2 points) a A child listens to the music from a trumpet. b A dog howls to the siren from a police car. c A person moves their arm when they hear the buzz of a fly. d Music comes out from a television speaker.
Answer:
d.music comes out from a television speaker
Explanation:
because television use electricity (electrical energy) and produce sound (sound energy) that we hear while watching tv
Answer:
The answer would be (D) Music comes out from a television speaker.
Explanation:
This is because the TV uses electrical energy from where its plugged in. And the speaker is the sound energy which is caused by the TV to go with the show you are watching.
Hope this helps!
Net force causes motion
Answer:
yes
Explanation:
If a 46 kg person walks up two floors in the Physics building (about 10 meters up), this person's potential energy has increased by _____ J.a. 1400 J b. 10,000 J. c. 1000 J. d. 100 J
Answer:
B. 10000 J
Explanation:
The possible answers are not related to the statement at all. The correct statement is:
If a 100 kg person walks up two floors in the Physics building (about 10 meters up), this person's potential energy has increased by:
From definitions of work and gravitational potential, we get the following formula to calculate the change experimented in the person's potential energy after walking up two floors in the Physics building:
[tex]\Delta U_{g} = m\cdot g \cdot \Delta z[/tex] (1)
Where:
[tex]\Delta U_{g}[/tex] - Change in the gravitational potential energy, measured in joules.
[tex]m[/tex] - Mass of the person, measured in kilograms.
[tex]g[/tex] - Gravitational acceleration, measured in meters per square second.
[tex]\Delta z[/tex] - Change in height, measured in meters.
If we know that [tex]m = 46\,kg[/tex], [tex]g = 9.807\,\frac{m}{s^{2}}[/tex] and [tex]\Delta z = 10\,m[/tex], then the change in the gravitational potential energy is:
[tex]\Delta U_{g} = (100\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)\cdot (10\,m)[/tex]
[tex]\Delta U_{g} = 9807\,J[/tex]
The choice that best approximates this answer is B.
An engineer is designing the runway for an airport. Of the planes that will use the airport, the lowest acceleration rate is likely to be 3 m/s2. The takeoff speed for this plane will be 65 m/s. All airplanes will start from rest(0m/s). Assuming this minimum acceleration, what is the minimum allowed length for the runway for take off?
Answer:
x = 704 [m]
Explanation:
To solve this problem we must use the following equation of kinematics.
[tex]v_{f} ^{2} =v_{o} ^{2} +2*a*x[/tex]
where:
Vf = final velocity = 65 [m/s]
Vo = initial velocity = 0 (starts from rest)
a = acceleration = 3 [m/s²]
x = distance [m]
Now replacing we have:
65² = 0 + 2*3*x
4225 = 6*x
x = 704 [m]
You use an electron microscope in which the matter wave associated with the electron beam has a wavelength of 0.0173 nm. What is the kinetic energy of an electron in the beam, expressed in electron volts?
Answer:
The kinetic energy of an electron in the beam is 5.04 keV.
Explanation:
We need to find the velocity of the electron by using the De Broglie wavelength:
[tex] \lambda = \frac{h}{mv} [/tex]
Where:
λ: is the wavelength = 0.0173 nm
v: is the velocity
m: is the electron's mass = 9.1x10⁻³¹ kg
h: is the Planck constant = 6.62x10⁻³⁴ J.s
[tex] v = \frac{h}{m\lambda} = \frac{6.62 \cdot 10^{-34} J.s}{9.1 \cdot 10^{-31} kg*0.0173 \cdot 10^{-9} m} = 4.21 \cdot 10^{7} m/s [/tex]
Now, we can find the kinetic energy:
[tex] E_{k} = \frac{1}{2}mv^{2} = \frac{1}{2}9.1 \cdot 10^{-31} kg*(4.21 \cdot 10^{7} m/s)^{2} = 8.06 \cdot 10^{-16} J*\frac{1 eV}{1.6 \cdot 10^{-19} J} = 5038 eV = 5.04 keV [/tex]
Therefore, the kinetic energy of an electron in the beam is 5.04 keV.
I hope it helps you!
How are the toes of a hen different from that of an eagle?
Answer:
no they different
Explanation:
because hen lives on land and eagle flies in sky it doesnt walk often just it aearch for its prey and it eats there only
Answer:
eheisjsnsndndj
Explanation:
sjdjdj
A typical elevator car with people has a mass of 1500.0 kg. Elevators are currently approaching speeds of 20.0 m/s - faster than the speed.
Required:
What is the upward force required if the elevator moves upward 200.0 meters before reaching 20.0 m/s?
Answer:
1500NExplanation:
Force = mass * acceleration
Given
Mass = 1500kg
Get the acceleration using the equation of motion;
v² = u²+2aS
20² = 0+2s(200)
400 = 400a
a = 400/400
a = 1m/s²
Get the upward force required
F = 1500 * 1
F = 1500N
Hence the upward force required if the elevator moves upward 200.0 meters before reaching 20.0 m/s is 1500N
The amount of time for a synchronous input to a flip-flop to be stable before the rising edge of clock is called the hold time. a) True b) False
Answer:
true
Explanation:
Answer:
true
Explanation:
Find the mass of an object on planet F if its weight is 650 N (g = 13m/s^2)
Answer:
the object's mass is 50 kg
Explanation:
We use Newton's second law to solve for the mass:
F = m * a , then m = F / a
In our case, the acceleration is the gravitational acceleration on the planet, and the force is the weight of the object on the planet. So we get:
m = w / a = 650 N / 13 m/s^2 = 50 kg
Then, the object's mass is 50 kg.
Just some Naruto couples having a Boxing Match.
Who do you think will win?! Naruto and Hinata or Pain and Konan?!
Answer:
naruto and hinata
Explanation:
Two particles are separated by 0.38 m and have charges of -6.25 x 10-9C
and 2.91 x 10-9 C. Use Coulomb's law to predict the force between the
particles if the distance is doubled. The equation for Coulomb's law is
Fe = kq92, and the constant, k, equals 9.00 x 10°N-m/c2.
A. -2.83 x 10-7N
B. 2.83 x 10-7N
C. -1.13 x 10-6N
D. 1.13 x 10-6N
Answer:A
Explanation:
Answer:
A. -2.83 x 10-7N
Explanation:
A 0.20-kg object is attached to the end of an ideal horizontal spring that has a spring constant of 120 N/m. The simple harmonic motion that occurs has a maximum speed of 0.70 m/s. Determine the amplitude A of the motion.
Answer:
The amplitude of the motion is 0.0286 m.
Explanation:
Given;
mass of the object, m = 0.2 kg
spring constant, k = 120 N/m
maximum speed of the simple harmonic motion, [tex]V_m[/tex] = 0.70 m/s
The amplitude A of the motion is given by;
[tex]V_m = \omega A\\\\[/tex]
where;
ω is the angular velocity given as;
[tex]\omega = \sqrt{\frac{k}{m} }\\\\\omega = \sqrt{\frac{120}{0.2} }\\\\\omega =24.5 \ rad/s[/tex]
Now, substitute the value of angular velocity and solve the amplitude;
[tex]V_m = \omega A\\\\A = \frac{V_m}{\omega}\\\\A = \frac{0.7}{24.5}\\\\A = 0.0286 \ m[/tex]
Therefore, the amplitude of the motion is 0.0286 m.
Show the relation among MA, VR and n.
Answer:
good luck!!! sorry I just needed the points xoxo
Explanation:
umm yeah no sorry I tried
The components of lifetime fitness include all of the following components except
Answer:it’s A
Explanation:
because i took the quiz
Answer:
D is the correct answer, not A
Explanation:
A vertical spring gun is used to launch balls into the air. If the spring is compressed by 4.9 cm, the ball of mass 5.5 g is launched to a maximum height 50.2 cm. How much should the spring be compressed to send the ball twice as high?
We know, by conservation of energy :
[tex]\dfrac{kx^2}{2}=mgh[/tex]
Therefore,
[tex]\dfrac{x_1^2}{x_2^2}=\dfrac{h_1}{h_2}[/tex]
Putting given values, we get :
[tex]\dfrac{x_1^2}{x_2^2}=\dfrac{h_1}{h_2}\\\\\dfrac{4.9^2}{x_2^2}=\dfrac{50.2}{2\times 50.2}\\\\x_2^2=2\times 4.9^2\\\\x_2 = 4.9\times \sqrt{2}\\\\x_2=6.93\ cm[/tex]
Therefore, the spring be compressed to 6.93 cm to send the ball twice as high.
Hence, this is the required solution.
g When the movable mirror of the Michelson interferometer is moved a small distance X while making a measurement, 246 fringes are counted moving into the field of the viewing mirror. What is X if the wavelength of the light entering the interferometer is 562 nm
Answer:
X = 69.1 x 10⁻⁶ m = 69.1 μm
Explanation:
The relationship between the motion of the moveable mirror and the fringe count of the Michelson's Interferometer is given by the following formula:
d = mλ/2
where,
d = distance moved by the mirror = X = ?
m = No. of Fringes counted = 246
λ = wavelength of light entering interferometer = 562 nm = 5.62 x 10⁻⁷ m
Therefore,
X = (246)(5.62 x 10⁻⁷ m)/2
Therefore,
X = 69.1 x 10⁻⁶ m = 69.1 μm
Protists are unique organisms that are so different from each other that they are sometimes called the 'junk drawer' kingdom.
True or False
Answer:
true
Explanation:
Im in k12 and I got an 100%
An object accelerates 12.0 m/s2 when a force of 6.0 newtons is applied to it. What is the mass of the object?
Answer:
0.5 kgExplanation:
The mass of the object can be found by using the formula
[tex]m = \frac{f}{a} \\ [/tex]
f is the force
a is the acceleration
From the question we have
[tex]m = \frac{6}{12} = \frac{1}{2} \\ [/tex]
We have the final answer as
0.5 kgHope this helps you
Which has a greater buoyant force on it, a 35.0-cm3 piece of wood floating with part of its volume above water or a 35.0-cm3 piece of submerged iron?
The iron has, because it's displacing more water than the wood is.
Bani wants to know that when a cold wooden spoon is dipped in a cup of hot milk, it transfers heat to its other end by the process of -
Conduction
Convection
Radiation
None of these
Answer:
Conduction is the movement of heat through a substance by the collision of molecules. ... This process continues until heat energy from the warmer object spreads throughout the cooler object, like the heat from the milk spreading throughout the wooden spoon dipped in it. Hence, Option Conduction is correct.
why is The sum of two vectors has the smallest magnitude when the angle between these two vectors is 180t
Answer:
C = A - B
Explanation:
The addition of vectors takes into account the magnitude of each vector and its direction, so when adding two vectors, the result depends on the direction of the vectors.
* If the vectors have the same direction the result is maximum
C = A + A
* if the vectors have 90 between them, the magnitude of the result is given by the Pythagorean Theorem
C = √(A² + B²)
* if the vectors have 180º between them the result is minimal
C = A - B
We can also perform this sum graphically, where the resulting vector goes from the origin of the first vector to the tip of the last one, it can clearly be seen that when the vectors are antiparallel (180º angle) the magnitude is minimal
A block with a mass M = 4.85 kg is resting on a slide that has a curved surface. There is no friction. The speed of the block after it has slid along the slide sufficiently far for its vertical drop to be 19.6 m is:__________a. 19.6 m/s b. 384 m/s c. 93 m/s d. 43.2 m/s e. The problem cannot be solved because the shape of the curved slide is not given.
Answer:
The correct option is a
Explanation:
From the question we are told that
The mass of the block is [tex]m = 4.84 \ kg[/tex]
The height of the vertical drop is [tex]h = 19.6 \ m[/tex]
Generally from the law of energy conservation , the potential energy at the top of the slide is equal to the kinetic energy at the point after sliding this can be mathematically represented as
[tex]PE = KE[/tex]
i.e [tex]m * g * h = \frac{1}{2} * m * v^2[/tex]
=> [tex]gh = 0.5 v^2[/tex]
=> [tex]v = \sqrt{\frac{9.8 * 19.6}{0.5 } }[/tex]
=> [tex]v = 19.6 \ m/s[/tex]
An artificial satellite in a circular orbit around the Sun has a period of 8 years. Determine the ratio of the satellite's orbital radius to that of the earth's orbital radius. Assume that the earth's orbit around the Sun is circular.
Answer:
The ratio is [tex]R_c:R_e = 4 : 1[/tex]
Explanation:
From the question we are told that
The period of the satellite is [tex]T_c = 8 \ years[/tex]
Generally the period of earth around the sun is [tex]T_e = 1 \ year[/tex]
Generally from Kepler's third law , which is mathematically represented as
[tex]\frac{T_c ^2}{T_e^2} = \frac{R_c^3}{R_e^3}[/tex]
Here [tex]R_c[/tex] is the radius of the orbit which the satellite rotate around the sun
[tex]R_e[/tex] is the radius of the orbit which the earth rotate around the sun
=> [tex]\frac{R_c^3}{R_e^3} = [\frac{8}{1} ]^2[/tex]
=> [tex]\frac{R_c}{R_e} = \sqrt[3]{[\frac{8}{1} ]^2}[/tex]
=> [tex]\frac{R_c}{R_e} = \frac{4}{1 }[/tex]
=> [tex]R_c:R_e = 4 : 1[/tex]
You wish to design a pendulum which moves a mass along an arc of length 40 cm when the angle with the vertical changes by 20 degrees. What should be the length L in meters of the pendulum? Enter the numerical answer without units. Your answer must be within 5% of the exact answer to receive credit.
Answer:
The length of the pendulum cord is approximately 114.592 centimeters.
Explanation:
We include a representation of the motion of the pendulum in the image attached below. The trajectory described by the pendulum is represented by the following geometrical expression:
[tex]s = \theta \cdot r[/tex] (1)
Where:
[tex]\theta[/tex] - Angular change with the vertical, measured in radians.
[tex]r[/tex] - Length of the pendulum cord, measured in centimeters.
[tex]s[/tex] - Arc, measured in centimeters.
If we know that [tex]\theta = \frac{\pi}{9}[/tex] and [tex]s = 40\,cm[/tex], then the length of the pendulum cord is.
[tex]r = \frac{s}{\theta}[/tex]
[tex]r = \frac{40\,cm}{\frac{\pi}{9} }[/tex]
[tex]r \approx 114.592\,cm[/tex]
The length of the pendulum cord is approximately 114.592 centimeters.
A child whose weight is 287 N slides down a 7.20 m playground slide that makes an angle of 31.0° with the horizontal. The coefficient of kinetic friction between slide and child is 0.120. (a) How much energy is transferred to thermal energy? (b) If she starts at the top with a speed of 0.559 m/s, what is her speed at the bottom?
Answer:
a
[tex]H =212.6 \ J[/tex]
b
[tex]v = 7.647 \ m/s[/tex]
Explanation:
From the question we are told that
The child's weight is [tex]W_c = 287 \ N[/tex]
The length of the sliding surface of the playground is [tex]L = 7.20 \ m[/tex]
The coefficient of friction is [tex]\mu = 0.120[/tex]
The angle is [tex]\theta = 31.0 ^o[/tex]
The initial speed is [tex]u = 0.559 \ m/s[/tex]
Generally the normal force acting on the child is mathematically represented as
=> [tex]N = mg * cos \theta[/tex]
Note [tex]m * g = W_c[/tex]
Generally the frictional force between the slide and the child is
[tex]F_f = \mu * mg * cos \theta[/tex]
Generally the resultant force acting on the child due to her weight and the frictional force is mathematically represented as
[tex]F =m* g sin(\theta) - F_f[/tex]
Here F is the resultant force and it is represented as [tex]F = ma[/tex]
=> [tex]ma = m* g sin(31.0) - \mu * mg * cos (31.0)[/tex]
=> [tex]a = g sin(31.0)- \mu * g * cos (31.0)[/tex]
=> [tex]a = 9.8 * sin(31.0) - 0.120 * 9.8 * cos (31.0)[/tex]
=>[tex]a = 4.039 \ m/s^2[/tex]
So
[tex]F_f = 0.120 * 287 * cos (31.0)[/tex]
=> [tex]F_f = 29.52 \ N[/tex]
Generally the heat energy generated by the frictional force which equivalent tot the workdone by the frictional force is mathematically represented as
[tex]H = F_f * L[/tex]
=> [tex]H = 29.52 * 7.2[/tex]
=> [tex]H =212.6 \ J[/tex]
Generally from kinematic equation we have that
[tex]v^2 = u^2 + 2as[/tex]
=> [tex]v^2 = 0.559^2 + 2 * 4.039 * 7.2[/tex]
=> [tex]v = \sqrt{0.559^2 + 2 * 4.039 * 7.2}[/tex]
=> [tex]v = 7.647 \ m/s[/tex]
A potter's wheel is a uniform disk of mass of 10.0 kg and radius 20.0 cm. A 2.0-kg lump of clay, roughly cylindrical with radius 3.0 cm, is placed at the center of the wheel. The wheel initially rotates at 30.0 rev/min. The clay then flattens into a disk of radius 8.0 cm. What is the final angular speed of the wheel?
a. 29.6 rev/min
b. 29.2 rev/min
c. 30.8 rev/min
d. 30.4 rev/min
e. 30.0 rev/min
Answer:
b. 29.2 rev/min
Explanation:
Assuming no external torques acting during the process, total angular momentum must be conserved, as follows:[tex]L_{0} = L_{f} (1)[/tex]
The initial angular momentum L₀, can be expressed as follows:[tex]L_{0} = I_{0} * \omega_{0} (2)[/tex]
where I₀ = initial moment of inertia = moment of inertia of the disk +
moment of inertia of the cylinder and ω₀ = initial angular velocity =
30.0 rev/min.
Replacing by the values, we get:[tex]I_{0} = \frac{1}{2} * m_{d} *r_{d} ^{2} + \frac{1}{2}* m_{c} *r_{c} ^{2} = 0.2 kg*m2 +9e-4 kg*m2 = 0.2009 kg*m2 (3)[/tex]⇒ L₀ = I₀* ω₀ = 0.2009 kg*m² * 30.0 rev/min = 6.027 kg*m²*rev/minThe final angular momentum can be written as follows:[tex]L_{f} = I_{f} * \omega_{f} (4)[/tex]
where If = final moment of inertia = moment of the inertia of the solid
disk + moment of inertia of the clay flattened on a disk, and ωf = final
angular velocity.
Replacing by the values, we get:[tex]I_{f} = \frac{1}{2} * m_{d} *r_{d} ^{2} + \frac{1}{2}* m_{fd} *r_{fd} ^{2} = 0.2 kg*m2 +6.4e-3 kg*m2 = 0.2064 kg*m2 (5)[/tex]
⇒ Lo =Lf = If*ωf
Replacing (2) in (1), and solving for ωf, we get:[tex]\omega_{f} = \frac{L_{o}}{I_{f} } = \frac{6.027kg*m2*rev/min}{0.2064kg*m2} = 29.2 rev/min (6)[/tex]
The rate of change of angular displacement is defined as angular speed. The final angular speed of the wheel will be 29.2 rev/min.
What is angular speed?The rate of change of angular displacement is defined as angular speed. is stated as follows:
ω = θ t
Where,
θ is the angle of rotation,
t is the time
ω is the angular speed
The given data in the problem is
m is the mass of wheel = 10.0 kg
r₁ is the radius of disk = 20.0 cm=0.2
M is the mass of clay= 2.0 kg
R is the radius of cylinder = 3.0cm
[tex]\rm \omega_i[/tex] is the initial rotational speed =30.0 rev/min
r₂ is the final radius of disk= 8.0 cm.
[tex]\rm \omega_f[/tex] is the initial rotational speed=?
When the external torques act on the body is zero the total angular momentum must be conserved, as follows:
Initial momentum = Final momentum
[tex]\rm L_0=L_f[/tex]
The value of the initial angular momentum L₀ is found by
I₀ = initial moment of inertia = moment of inertia of the disk +moment of inertia of the cylinder
[tex]\rm I_0= \frac{1}{2}m_dr_d^2+ \frac{1}{2}m_cr_c^2\\\\ \rm I_0= \frac{1}{2}\times 10\times (0.2)^2+ \frac{1}{2}\times m_2(0.03)^2[/tex]
[tex]\rm L_0 = I_0\times \omega_0\\\\ L_0 = 2009\times 30\\\\ \rm L_0 =6.027 \;kgm^2rev/min[/tex]
The value of the final angular momentum [tex]I_f[/tex] is found by
[tex]\rm I_f= \frac{1}{2}m_dr_d^2+ \frac{1}{2}m_fr_fd^2\\\\ \rm I_0= 0.2064 m_2[/tex]
[tex]\rm I_f[/tex] is the final moment of inertia = moment of the inertia of the solid disk + moment of inertia of the clay flattened on a disk.
[tex]L_0 =L_f = I_f \times \omega_f[/tex]
[tex]\rm \omega_f=\frac{L_0}{I_f} \\\\ \rm \omega_f=\frac{6.027 m_2}{0.2064 m_2} \\\\ \rm \omega_f= 29.2\; rev/min[/tex]
Hence the final angular speed of the wheel will be 29.2 rev/min.
To learn more about the angular speed refer to the link;
https://brainly.com/question/9684
Answered: A 4 kg mass is attached to a horizontal spring with the spring constant of 600 N/m and rests on a frictionless surface on the ground. The spring is compressed 0.5 m past its equilibrium. What is the initial energy of the system.
Answer: 75 joules
During a safety crash, a car impacts a solid concrete barrier and and comes to rest in 0.10s. In a second test, an identical car traveling at the same initial speed impacts a line of water barrels and comes to rest in 2.3s. During which test was the change in the momentum of the car the greatest?
a. It is the same for both cars.
b. The car that hits the concrete barrier.
c. The car that hits the water barrels
Answer:
The correct answer is C
Explanation:
Change is momentum can be described as the change in the product of mass and velocity of a body. Every moving object as a momentum and the higher the momentum of this object, the harder it is to stop. Impulse (a force), which is sometimes used to describe change in momentum can be described as the product as force multiplied by time.
From the description above, it can be deduced that an increase in impulse can lead to a greater change in momentum. And an increase in impulse can be brought about by an increase in the time it takes a body to be brought to rest after collision. And since the car that hit the water barrels was brought to rest at a longer time, it has a greater change in momentum
A cyclist is riding along at a speed of 20.7 when she decides to apply the brakes which gave a deceleration applied was a rate of -3.4 m/s2 over the span of 7.8 s. What distance does she travel over that period of time.
Answer:
The distance is 58.03 m
Explanation:
Constant Acceleration Motion
It occurs when the velocity of an object changes by an equal amount in every equal period of time.
Being a the constant acceleration, vo the initial speed, vf the final speed, and t the time, the following relation applies:
[tex]v_f=v_o+at[/tex]
The distance traveled by the object is given by:
[tex]\displaystyle x=v_o.t+\frac{a.t^2}{2}[/tex]
The conditions of the problem state the cyclist has an initial speed of v0=20.7 m/s during t=7.8 seconds and acceleration of -3.4 m/s^2.
The final speed is:
[tex]v_f=20.7+(-3.4)\cdot 7.8[/tex]
[tex]v_f=20.7-26.52[/tex]
[tex]v_f=-5.82\ m/s[/tex]
Note the cyclist has stopped and come back because his speed is negative. Now calculate the distance:
[tex]\displaystyle x=20.7\cdot 7.8+\frac{(-3.4)\cdot 7.8^2}{2}[/tex]
[tex]\displaystyle x=161.46-103.43[/tex]
x=58.03 m
Two parallel 3.0-meter long wires conduct current. The current in the top wire is 12.5 A and flows to the right. The top wire feels a repulsive force of 2.4 x 10^-4 N created by the interaction of the 12.5 A current and the magnetic field created by the bottom current (I). Find the magnitude and direction of the bottom current.
Complete question:
Two parallel 3.0-meter long wires conduct current. The current in the top wire is 12.5 A and flows to the right. The top wire feels a repulsive force of 2.4 x 10^-4 N created by the interaction of the 12.5 A current and the magnetic field created by the bottom current (I). Find the magnitude and direction of the bottom current, if the distance between the two wires is 40cm.
Answer:
The bottom current is 12.8 A to the right.
Explanation:
Given;
length of the wires, L = 3.0 m
current in the top wire, I₁ = 12.5 A
repulsive force between the two wires, F = 2.4 x 10⁻⁴ N
distance between the two wires, r = 40 cm = 0.4 m
The repulsive force between the two wires is given by;
[tex]F = \frac{\mu_oI_1I_2L}{2\pi r}\\\\I_{2} = \frac{2F\pi r}{\mu_oI_1L}[/tex]
Where;
I₂ is the bottom current
The direction of the bottom current must be in the same direction as the top current since the force between the two wires is repulsive.
[tex]I_{2} = \frac{2F\pi r}{\mu_oI_1L}\\\\I_{2} = \frac{2(2.4*10^{-4})(\pi)(0.4)}{(4\pi*10^{-7})(12.5)(3)}\\\\I_{2} = 12.8 \ A[/tex]
Therefore, the bottom current is 12.8 A to the right.