General Physics – Faraday Practice
1. A uniform magnetic field of 6x10-3 T is created within the center of a solenoid connected to a voltage source. Answer the following questions using the concept of induced voltages.
a) A circular wire hoop of radius 0.3 m is dropped from above the solenoid so that the axis of the hoop remains along the axis of the solenoid. If the magnetic field where the hoop is dropped can be ignored, and the wire hoop takes 1.3 seconds to reach the center of the solenoid, then estimate the magnitude of the induced EMF.
b) What is the direction of the induced current? Briefly describe your reasoning.
c) Inside the solenoid, the magnetic field maintains a constant value. What is the induced EMF while the hoop is falling inside the solenoid, assuming it takes about 0.5 seconds for the hoop to travel along the length of the solenoid?
d) Calculate the direction and magnitude of the EMF induced in the wire loop as it falls out the bottom of the solenoid. Assume it takes about 0.3 seconds for the hoop to fall from the middle of the magnet to a region in which the field drops to zero.
V
2. In an NMR laboratory, a magnet usually sits on one side of the room, and the
instrumentation is set on the other side of the room because the field around
the magnet is high. Usually if you go a few feet from the magnet, the field
will decrease significantly from the maximum value.
Consider the diagram below showing a magnet on one side of a room and the magnetic field (going into the paper) around it. Imagine you take a square rectangular loop of wire (10 cm X 10 cm)with a resistance of 20 W from the side of the room near the magnet to the other side. Initially you are in a region where the magnetic field is B= 0.9 T (on the right side). As you walk away from the magnet, the magnetic field decreases uniformly until you reach a region in which B= 0.1 T. The time it takes to walk from one region to the other is 4 seconds. Answer the following questions for the scenario pictured below.
a)What is the initial flux through the rectangular loop when it is near the magnet?
b) Calculate the final flux through the loop when it is in the lower field region shown on the left.
c) Find the induced EMF and the current (magnitude and direction) through the loop for the above situation.
d) What travel time Dt (from one region to the other) would be required in order to induce an EMF of 12 Volts in the loop?
3. Faraday’s Law. Consider a current carrying wire placed next to a 0.1 m square loop of wire. Since the wire is a flow of charges, a magnetic field forms within the loop. Assume that when the current flows a uniform field of 1 x10-4 T exists inside the loop. If the current through the wire is stopped, then the field inside the loop will decrease to zero with time: for the situation depicted below, assume the magnetic field decreases to zero exponentially as B(t)= (1 x10-4 T)e-t/1ms.
a) Find the flux through the square loop as a function of time.
b) Calculate the magnitude and direction of the EMF induced in the loop.
c) If the square loop has a resistance of 20 W, then find the current induced in the loop.
d) How much power is dissipated in the loop?
4. A length of wire with a resistance of 50 W is coiled around a 0.03 m long cylindrical former into 20 circular loops of radius 0.15 m (like a solenoid). Initially a bar magnet is placed inside the coils producing a uniform magnetic field of 5x10-3 T pointing upward along the axis of the cylinder.
a) What is the initial flux through the coils?
b) Calculate the flux through the coils if the magnet is taken out of the cylindrical coils.
c) If the magnet is removed from the coil in 0.75 seconds, then calculate the EMF which develops along the wire.
d) Draw a diagram of the situation described showing the orientation of the coils with the field. Show the direction of the EMF on this drawing.
e) Calculate the current through the wire.
5. Consider a rectangular current loop with a sliding bar extending over it which is placed in an external magnetic field in the orientation shown in the diagram below. The loop has a width of L and the bar initially rests a distance A from the closed end of the rectangle. At some point in time the bar is forced to oscillate sinusoidally about its initial position. In particular, the displacement about its position a distance A from the end is given by
X=xosinwt where xo < A.
a) Calculate the magnetic flux through the closed loop shown in the picture.
b) Find the EMF induced in the closed circuit.
c) In which direction will the conventional current flow when the bar moves to the right?
d) Consider using the above set-up to generate AC power. In particular: if L=0.3 m, A = 0.4 cm, and B=1 T then what must be the peak displacement xo to provide a peak EMF of 120 V at a frequency w/2p=60 s-1.
C B A
6.
A rectangular loop of wire is free to bend back and forth in the wind as shown
below.
The loop has dimensions of length equal to 0.5 m, and width 0.2 m and lies in a magnetic field of 0.5 T pointing straight up. For the purposes of this problem, assume it starts from position A (where the vector normal to the loop is 40 o to the field), moves to position B in which the plane of the loop lies along the B-field, and finally moves to position C (where the angle between the vector normal to the loop and the field is 30o).
a)What is the initial flux through the loop in position A?
b) What is the flux through the loop in position B?
c) Calculate the direction and magnitude of the average EMF induced in the loop in moving from A to B? Briefly describe how you determined the direction of the EMF on a separate drawing!
d) What is the flux when the loop is in position C?
e) What is the magnitude and direction of the average EMF produced in going from B to C?
f) If the loop has a resistance of 12 W, find the current induced from A to B, and them from B to C.
5. Ring toss: An electromagnet is set up to produce a magnetic field up with magnitude given in the drawing below. A ring with a resistance of 20 W and a radius of 0.18 m drops horizontally down over the coils of the electromagnet to the positions labeled by A, B, and C. Note that the strength of the magnetic field increases as the ring falls. It takes 0.85 s for the ring to fall from A to B, and 0,45 s to get from B to C.
a)Calculate the flux through the ring at the position labeled A.
b) Find the average EMF induced as the ring travels from A to B. Include the direction as part of your solution.
c) What is the average current induced as the ring falls
from B to C. Include direction.
d) In terms of time, how fast would the ring have to fall from A to C in order to produce an average EMF of 12 V?
e) Calculate the emf at the bottom of the magnet if it has been sitting at this location for 5 s.
f) The ring sets at the bottom of the magnet in the field shown at position C. If the voltage is cut off, the field will drop to zero in 0.007 s. Calculate the average induced current being sure to include a direction