Bilkent University     Department of Physics

PHYS 112 Electricity and Magnetism

Spring 2012 Homework Assignments

Homework Policy

• Homework 1: (due Monday Feb. 20 2012)
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Consider a dipole made up of a charge +q at the (x,y,z) coordinate (0,0,a/2) and a charge -q at (0,0, -a/2).

The dipole moment is then p = aq.

Find the electric field at a point (x,0,z) far away from the origin. You should consider the limit when r >> a

where r2 = x2 + z2.  Express your result in terms of r and θ, where θ is the angle between the x-axis and

the position at (x,0,z):   tan(θ) = z/x  so that  x = r cos(θ)  and  z = r sin(θ).

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• Homework 2: (due Monday Feb. 27 2012)
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A spherically symmetric charge of radius R has a charge density (per unit volume)  equal to ρ(r).

(a) What must ρ(r) be so that the field inside ( r < R ) has a constant magnitude E0 ?

(b) What is the total charge in a volume of radius r ?

(c) Plot the quantities in parts (a) and (b) for all values of r.

Repeat the parts (a), (b), and (c) above for an infinitely long cylindrical charge of radius R.

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• Homework 3: (due Monday March 5 2012)
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Consider the two geometries in Homework 2. In both cases, assume that the potential at r = 0 is equal to zero.

For both cases, find the potential as a function of r, and plot your results.

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• Homework 4: (due Monday April 9 2012)
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Find the magnetic field on the axis of a rotating thin charged disk. The insulating disk is uniformly

charged with a surface charge density (per unit area) σ  and has a radius R. The disk is rotating

with angular velocity ω.

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Check the Stars system for your homework grade. In some cases, you may be able to re-submit your homework to the assistant with corrections and improve your grade.