Electricity and Magnetism: PHY-204
Fall Semester 2014
Tutoring Session 12: Time-Varying Magnetic and Electric
Fields
1. A long, straight wire carries a current given by I = Imax sin(ωt + ϕ). The wire lies in
the plane of a rectangular coil of N turns of wire as shown below. The quantities Imax ,
ω and ϕ are all constants. Determine the emf induced in the coil by the magnetic field
created by the current in the straight wire.
2. A thin wire of length l is held parallel to and a distance d above a long, thin wire
carrying current I, as shown below. The long wire has a fixed position. The wire of
length l is released at instant t = 0 and falls, remaining parallel to the current-carrying
wire as it falls. Assume the falling wire accelerates at ⃗g m/s2 . Derive an equation for
the emf induced in it as a function of time.
3. A rectangular loop of area A is placed in a region where the magnetic field is perpendicular to the plane of the loop. The magnitude of the field is allowed to vary in
time according to B = Bmax e−t/τ , where Bmax and τ are constants. The field has the
constant value Bmax for t < 0. Find the emf induced in the loop as a function of time.
Date: 10 December, 2014
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Electricity and Magnetism: PHY-204
Fall Semester 2014
4. Two infinitely long solenoids (shown in cross section) pass through a circuit as shown
⃗ inside each solenoid is the same and is increasing at the
below. The magnitude of B
rate of 100 T /s. What is the current in each resistor?
5. In the figure below, a semi-circular conductor of radius R is rotated about the axis
AC at a constant rate of ω rev/min. A uniform magnetic field of magnitude B fills
the entire region below the axis and is directed out of the page.
(a) Calculate the maximum value of the emf induced between the ends of the conductor.
(b) How will your answer to part (a) change if the magnetic field were allowed to
extend a distance R above the axis of rotation?
(c) Sketch the emf versus time when the field is as drawn in the figure above and
when the field is extended as described in part (b).
Date: 10 December, 2014
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Electricity and Magnetism: PHY-204
Fall Semester 2014
6. A current I is charging a capacitor that has circular plates of radius b as shown below.
If the plate separation is s what is the time rate of increase of electric field between
the plates? What is the magnetic field between the plates at the point P , a distance
r from the center? You may assume that the distance s between the plates is small
compared to their radius b.
Date: 10 December, 2014
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