Question 1

A metal rod of length L in a region of space where a constant magnetic field points into the page rotates clockwise about an axis through its center at constant angular velocity  $ \omega $.While it rotates,the point(s)at lowest potential is(are)

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Question 2

Starting outside the region with the magnetic field,a single square coil of wire moves across the region with a uniform magnetic field $\vec { B }$ perpendicular to the page.The loop moves at constant velocity $\overrightarrow { \mathbf { v } }$ .As seen from above,a counterclockwise emf is regarded as positive.Roger claims that the graph shown below represents the induced emf.Martin says he's wrong.In which direction did the loop move over the plane of the page,or is Martin correct?

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Question 3

In a demonstration,a 4.00 cm² square coil with 10 000 turns enters a larger square region with a uniform 1.50 T magnetic field at a speed of 100 m/s.The plane of the coil is perpendicular to the field lines.If the breakdown voltage of air is 4 000 V/cm on that day,the largest gap you can have between the two wires connected to the ends of the coil and still get a spark is

Accepted Answer

The induced emf (electromotive force) in the coil can be calculated using Faraday's law of electromagnetic induction. The change in magnetic flux is given by the product of the magnetic field, the area of the coil, and the number of turns. The induced emf is then the rate of change of this flux as the coil enters the magnetic field. The breakdown voltage of air is given, and the largest gap for a spark is determined by dividing the induced emf by the breakdown voltage per cm.

Question 4

As shown below,a square loop of wire of side a moves through a uniform magnetic field of magnitude B perpendicular to the page at constant velocity $\overrightarrow { \mathbf { v } }$ directed to the right.Judd says that the emf induced in the loop is zero.Roger claims that it has magnitude B $\ell v$ .Which one,if either,is correct,and why?

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Question 5

Starting outside the region with the magnetic field,a single square coil of wire enters,moves across,and then leaves the region with a uniform magnetic field $\vec { B }$ perpendicular to the page so that the graph shown below represents the induced emf.The loop moves at constant velocity $\overrightarrow { \mathbf { v } }$ .As seen from above,a counterclockwise emf is regarded as positive.In which direction did the loop move over the plane of the page?

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Question 6

What is the inductance of a series RL circuit in which R = 1.0 K$\Omega$if the current increases to one-third of its final value in 30 $\mu$s?

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The time constant τ for an RL circuit is given by τ = L/R. The current reaches one-third of its final value at t = τ * ln(3). Given R = 1000 Ω and t = 30 μs, solve for L: L = R * t / ln(3) = 1000 * 30e-6 / ln(3) ≈ 74 mH.

Question 7

A long solenoid has a radius of 4.0 cm and has 800 turns/m.If the current in the solenoid is increasing at the rate of 3.0 A/s,what is the magnitude of the induced electric field at a point 2.2 cm from the axis of the solenoid?

Accepted Answer

The magnitude of the induced electric field at a point 2.2 cm from the axis of the solenoid is given by:$$E = \frac{d\Phi_B}{dt} = \frac{d}{dt}(\mu_0 n I A)$$where:* $d\Phi_B/dt$ is the rate of change of magnetic flux* $\mu_0$ is the permeability of free space* $n$ is the number of turns per unit length* $I$ is the current* $A$ is the area of the solenoidSubstituting the given values into the equation, we get:$$E = \frac{d}{dt}(\mu_0 n I A) = \mu_0 n \frac{dI}{dt} A = (4\pi 	imes 10^{-7} 	ext{ T$\cdot$m/A})(800 	ext{ turns/m})(3.0 	ext{ A/s})(\pi (0.022 	ext{ m})^2) = 3.3 	imes 10^{-5} 	ext{ V/m}$$Therefore, the magnitude of the induced electric field at a point 2.2 cm from the axis of the solenoid is 3.3 x 10^-5 V/m.

Question 8

A long solenoid (radius = 3.0 cm,2 500 turns per meter)carries a current given by I = 0.30 sin(200 $\pi$t)A,where t is measured in s.When t = 5.0 ms,what is the magnitude of the induced electric field at a point which is 2.0 cm from the axis of the solenoid?

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Question 9

As shown below,a square loop of wire of side a moves through a uniform magnetic field of magnitude B perpendicular to the page at constant velocity $\overrightarrow { \mathbf { v } }$ directed to the right.Which statement regarding the electric field induced in the wires is correct for the wires at the left and right sides of the loop?

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Question 10

An electric field of 4.0 $\mu$V/m is induced at a point 2.0 cm from the axis of a long solenoid (radius = 3.0 cm,800 turns/m).At what rate is the current in the solenoid changing at this instant?

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Question 11

For the circuit shown,what is the rate of change of the current in the inductor when the current in the battery is 0.50 A?

Accepted Answer

Using Kirchhoff's voltage law, we can write:

V_battery - L(di/dt) - IR = 0

where V_battery is the emf of the battery, L is the inductance, i is the current in the inductor, R is the resistance, and di/dt is the rate of change of current in the inductor.

When the current in the battery is 0.50 A, we have:

V_battery = IR + L(di/dt)

since there is no voltage drop across the resistor.

Taking the derivative of both sides with respect to time, we get:

0 = R(di/dt)^2 + L(d^2i/dt^2)

Rearranging and solving for d^2i/dt^2, we get:

d^2i/dt^2 = (-R/L)(di/dt)

Substituting the values given in the problem, we have:

d^2i/dt^2 = (-4 Ω)/(0.04 H)(0.50 A) = -200 A/s^2

Taking the absolute value, we get:

|d^2i/dt^2| = 200 A/s^2

Therefore, the rate of change of the current in the inductor when the current in the battery is 0.50 A is 200 A/s. The correct answer is (C).

Question 12

Coaxial Cable A has twice the length,twice the radius of the inner solid conductor,and twice the radius of the outer cylindrical conducting shell of coaxial Cable B.What is the ratio of the inductance of Cable A to that of Cable B?

Accepted Answer

Inductance is proportional to the natural logarithm of the ratio of the outer radius to the inner radius. 
L ∝ ln(b/a)

For cable A: 
Let the inner radius be r1 A and outer radius be r2 A. 
Length = 2L and r1 A = 2r1 B and r2 A = 2r2 B

So, b/a for cable A = (2r2 A)/(2r1 A) = r2 A/r1 A 
And b/a for cable B = r2 B/r1 B

So, the ratio of their inductances L_A/L_B = ln(r2 A/r1 A)/ln(r2 B/r1 B) 
= ln[(2r2 B)/(2r1 B)]/ln(r2 B/r1 B) 
= ln2/ln2 
= 2

Hence, the ratio of the inductance of Cable A to that of Cable B is 2.

Question 13

Two bulbs are shown in a circuit that surrounds a region of increasing magnetic field directed out of the page.When the switch is closed,

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Question 14

A long solenoid (radius = 3.0 cm,2 500 turns per meter)carries a current given by I = 0.30 sin(200 t)A,where t is measured in s.When t = 2.5 ms,what is the magnitude of the induced electric field at a point which is 4.0 cm from the axis of the solenoid?

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The answer of A long solenoid (radius = 3.0 cm,2...

Question 15

Two bulbs are shown in a circuit that surrounds a region of increasing magnetic field directed out of the page.When the switch is closed,

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Question 16

A metal rod of length L in a region of space where a constant magnetic field points into the page rotates clockwise about an axis through its center at constant angular velocity  $ \omega $.While it rotates,the point(s)at highest potential is(are)

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The answer of A metal rod of length L in...

Question 17

Which of the following are the units of a henry and a farad respectively?

Accepted Answer

The henry is the unit of inductance and is defined as the electromotive force (emf) induced in a circuit when the current through the circuit changes at a rate of one ampere per second. The farad is the unit of capacitance and is defined as the capacitance of a capacitor that stores one coulomb of charge when one volt is applied across it.

Question 18

A long solenoid has a radius of 2.0 cm and has 700 turns/m.If the current in the solenoid is decreasing at the rate of 8.0 A/s,what is the magnitude of the induced electric field at a point 2.5 cm from the axis of the solenoid?

Accepted Answer

The magnitude of the induced electric field at a point 2.5 cm from the axis of the solenoid is given by:$$E = \frac{\mu_0 N}{2\pi r}\frac{dI}{dt}$$where:* $\mu_0$ is the permeability of free space ($4\pi 	imes 10^{-7} 	ext{ T}\cdot	ext{m/A}$)* $N$ is the number of turns per unit length (700 turns/m)* $r$ is the distance from the axis of the solenoid (2.5 cm = 0.025 m)* $dI/dt$ is the rate of change of current (-8.0 A/s)Plugging in these values, we get:$$E = \frac{(4\pi 	imes 10^{-7} 	ext{ T}\cdot	ext{m/A})(700 	ext{ turns/m})}{2\pi (0.025 	ext{ m})}(-8.0 	ext{ A/s}) = 56 \mu	ext{V/m}$$Therefore, the correct answer is A.

Question 19

Starting outside the region with the magnetic field,a single square coil of wire enters,moves across,and then leaves the region with a uniform magnetic field $\vec { B }$ perpendicular to the page so that the graph shown below represents the induced emf.The loop moves at constant velocity $\overrightarrow { \mathbf { v } }$ .As seen from above,a counterclockwise emf is regarded as positive.In which direction did the loop move over the plane of the page?

Accepted Answer

The answer of Starting outside the region with the magnetic...

Question 20

Two bulbs are shown in a circuit that surrounds a region of increasing magnetic field directed out of the page.When the switch is open, the page.When the switch is closed,

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The answer of Two bulbs are shown in a circuit...

Quiz 23: Faradays Law and Inductance

What is the inductance of a series RL circuit in which R = 1.0 K $\Omega$ if the current increases to one-third of its final value in 30 $\mu$ s?

A long solenoid has a radius of 4.0 cm and has 800 turns/m.If the current in the solenoid is increasing at the rate of 3.0 A/s,what is the magnitude of the induced electric field at a point 2.2 cm from the axis of the solenoid?

A long solenoid (radius = 3.0 cm,2 500 turns per meter) carries a current given by I = 0.30 sin(200 $\pi$ t) A,where t is measured in s.When t = 5.0 ms,what is the magnitude of the induced electric field at a point which is 2.0 cm from the axis of the solenoid?

An electric field of 4.0 $\mu$ V/m is induced at a point 2.0 cm from the axis of a long solenoid (radius = 3.0 cm,800 turns/m) .At what rate is the current in the solenoid changing at this instant?

For the circuit shown,what is the rate of change of the current in the inductor when the current in the battery is 0.50 A?

Coaxial Cable A has twice the length,twice the radius of the inner solid conductor,and twice the radius of the outer cylindrical conducting shell of coaxial Cable B.What is the ratio of the inductance of Cable A to that of Cable B?

Two bulbs are shown in a circuit that surrounds a region of increasing magnetic field directed out of the page.When the switch is closed,

A long solenoid (radius = 3.0 cm,2 500 turns per meter) carries a current given by I = 0.30 sin(200 t) A,where t is measured in s.When t = 2.5 ms,what is the magnitude of the induced electric field at a point which is 4.0 cm from the axis of the solenoid?

Two bulbs are shown in a circuit that surrounds a region of increasing magnetic field directed out of the page.When the switch is closed,

Which of the following are the units of a henry and a farad respectively?

A long solenoid has a radius of 2.0 cm and has 700 turns/m.If the current in the solenoid is decreasing at the rate of 8.0 A/s,what is the magnitude of the induced electric field at a point 2.5 cm from the axis of the solenoid?

Two bulbs are shown in a circuit that surrounds a region of increasing magnetic field directed out of the page.When the switch is open, the page.When the switch is closed,

Quiz 23: Faradays Law and Inductance

A metal rod of length L in a region of space where a constant magnetic field points into the page rotates clockwise about an axis through its center at constant angular velocity ω \omega ω .While it rotates,the point(s) at lowest potential is(are)

What is the inductance of a series RL circuit in which R = 1.0 K Ω\OmegaΩ if the current increases to one-third of its final value in 30 μ\muμ s?

A long solenoid has a radius of 4.0 cm and has 800 turns/m.If the current in the solenoid is increasing at the rate of 3.0 A/s,what is the magnitude of the induced electric field at a point 2.2 cm from the axis of the solenoid?

A long solenoid (radius = 3.0 cm,2 500 turns per meter) carries a current given by I = 0.30 sin(200 π\piπ t) A,where t is measured in s.When t = 5.0 ms,what is the magnitude of the induced electric field at a point which is 2.0 cm from the axis of the solenoid?

An electric field of 4.0 μ\muμ V/m is induced at a point 2.0 cm from the axis of a long solenoid (radius = 3.0 cm,800 turns/m) .At what rate is the current in the solenoid changing at this instant?

For the circuit shown,what is the rate of change of the current in the inductor when the current in the battery is 0.50 A?

Coaxial Cable A has twice the length,twice the radius of the inner solid conductor,and twice the radius of the outer cylindrical conducting shell of coaxial Cable B.What is the ratio of the inductance of Cable A to that of Cable B?

Two bulbs are shown in a circuit that surrounds a region of increasing magnetic field directed out of the page.When the switch is closed,

A long solenoid (radius = 3.0 cm,2 500 turns per meter) carries a current given by I = 0.30 sin(200 t) A,where t is measured in s.When t = 2.5 ms,what is the magnitude of the induced electric field at a point which is 4.0 cm from the axis of the solenoid?

Two bulbs are shown in a circuit that surrounds a region of increasing magnetic field directed out of the page.When the switch is closed,

A metal rod of length L in a region of space where a constant magnetic field points into the page rotates clockwise about an axis through its center at constant angular velocity ω \omega ω .While it rotates,the point(s) at highest potential is(are)

Which of the following are the units of a henry and a farad respectively?

A long solenoid has a radius of 2.0 cm and has 700 turns/m.If the current in the solenoid is decreasing at the rate of 8.0 A/s,what is the magnitude of the induced electric field at a point 2.5 cm from the axis of the solenoid?

Two bulbs are shown in a circuit that surrounds a region of increasing magnetic field directed out of the page.When the switch is open, the page.When the switch is closed,

What is the inductance of a series RL circuit in which R = 1.0 K $\Omega$ if the current increases to one-third of its final value in 30 $\mu$ s?

A long solenoid (radius = 3.0 cm,2 500 turns per meter) carries a current given by I = 0.30 sin(200 $\pi$ t) A,where t is measured in s.When t = 5.0 ms,what is the magnitude of the induced electric field at a point which is 2.0 cm from the axis of the solenoid?

An electric field of 4.0 $\mu$ V/m is induced at a point 2.0 cm from the axis of a long solenoid (radius = 3.0 cm,800 turns/m) .At what rate is the current in the solenoid changing at this instant?