Exam 23: Faradays Law and Inductance

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?

A conducting rod (length = 2.0 m)spins at a constant rate of 2.0 revolutions per second about an axis that is perpendicular to the rod and through its center.A uniform magnetic field (magnitude = 8.0 mT)is directed perpendicularly to the plane of rotation.What is the magnitude of the potential difference between the center of the rod and either of its ends?

A 5-turn square loop (10 cm along a side,resistance = 4.0 $\Omega$ )is placed in a magnetic field that makes an angle of 30 $\degree$ with the plane of the loop.The magnitude of this field varies with time according to B = 0.50t²,where t is measured in s and B in T.What is the induced current in the coil at t = 4.0 s?

A long solenoid (n = 1 500 turns/m)has a cross-sectional area of 0.40 m² and a current given by I = (4.0 + 3.0t²)A,where t is in seconds.A flat circular coil (N = 300 turns)with a cross-sectional area of 0.15 m² is inside and coaxial with the solenoid.What is the magnitude of the emf induced in the coil at t = 2.0 s?

A conducting rectangular loop of mass M,resistance R,and dimensions a *b is allowed to fall from rest through a uniform magnetic field which is perpendicular to the plane of the loop.The loop accelerates until it reaches a terminal speed (before the upper end enters the magnetic field).If a = 2.0 m,B = 6.0 T,R = 40 $\Omega$ ,and M = 0.60 kg,what is the terminal speed?

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

The switch in the figure is closed at t = 0 when the current I is zero.When I = 15 mA,what is the potential difference across the inductor?

A rectangular coil of 100 turns measures 40.0 cm by 20.0 cm.This coil is placed next to an electromagnet which is switched on,increasing the magnetic field through the coil from zero to 0.800 T in 50.0 ms.If the resistance of the coil is 2.0 ohms,what are the induced voltage and current in the coil?

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?

A bolt of lightning strikes the ground 200 m from a 100-turn coil oriented vertically and with the plane of the coil pointing toward the lightning strike.The radius of the coil is 0.800 m and the current in the lightning bolt falls from 6.02 *10⁶ A to zero in 10.5 $\mu$ s.What is the voltage induced in the coil over this time period? [A question for future electrical engineers: is there any way to get lightning to strike repeatedly at the same point?]

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?

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?

The magnetic field in a superconducting solenoid is 3.0 T.How much energy per unit volume is stored in the solenoid,in J/m³? $\mu$ ₀ = 4 $\pi$ *10 ^{- 7} T . A/m

A circuit contains two inductors of 6.0 mH inductance in parallel placed in series with an inductor of 8.0 mH inductance.After one of the 6.0 mH inductors burns out,the repairman wants to replace all three inductors with one inductor of equivalent inductance.Assuming inductors combine in series and parallel the same way resistors do,what inductance should he use?

A rectangular loop (area = 0.15 m²)turns in a uniform magnetic field with B = 0.20 T.At an instant when the angle between the magnetic field and the normal to the plane of the loop is ( $\pi$ /2)rad and increasing at the rate of 0.60 rad/s,what is the magnitude of the emf induced in the loop?

A metal blade spins at a constant rate of 5.0 revolutions per second about a pivot through one end of the blade.This rotation occurs in a region where the component of the earth's magnetic field perpendicular to the blade is 30 $\mu$ T.If the blade is 60 cm in length,what is the magnitude of the potential difference between its ends?