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PHYSICS 8B –  Fall 2015

MT1 practice problems

Problem 1 –  Electric field

Let’s consider a discrete distribution of 4 point-charges located at A(2d ;0), B(-2d ;0), C(0 ;-d) and D(0 ;d). The numbers in parentheses next to the points indicate the

point’s x- and y-positions, and d is a length. A  and B  each carry a charge -q, whereas C   and D  carry charges +2q  and +q,respectively.a) Draw, qualitatively, the 4 individual electric field vectors created by each of thecharges at point O, the origin, as well as the resulting electric field vector at O.

b) Calculate the vector )(O E  . 

c) Do you know another way of getting the electric field? You don’t need to makethe calculation.

Problem 2 –  Electric potential

A non-conducting sphere of radius R1  is surrounded by a larger but ultrathinspherical shell of radius R2. The volume charge density of the inner sphere is

  1(r)=ar  (a>0).

a)  Calculate the surface charge density  2 of the outer sphere such that its netcharge is twice that of the inner sphere.

b)  Calculate the electric field created at any point by this charge distribution.c)  Make a qualitative plot of the electric field as a function of the distance from

the center of the spheres. d)  Calculate the electric potential created at any point.

Problem 3 –  Current and resistance

a)  The Tevatron at Fermilab is designed to carry a beam of protons of current Itraveling at speed v  around a ring of radius R. Calculate the number N   ofprotons in the beam.

b)  A wire of total length 2L  consists of two equally long pieces of wire, one

made of copper (  Cu) and the other made of aluminum (   Al). Both wires havesame diameter d, and a voltage V   is applied across the length of the

composite wire. What is the current I  passing through the wire? 

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