EMF Exercise Class 4
1.
A long plastic rod has radius a.
Charge is uniformly distributed inside such that the total
charge per unit length = .
Show that the potential difference between a point on the
axis of the rod and a point outside the rod at radius r is
V 
Hints:

40

 r 
1

2Ln
 

 a 

- Draw side-view and axial view diagrams
- Find E for r < a and r > a (see Assignment 3)
- Split the integral for V into two parts
2.
In a certain region, the electric potential is
V(x,y,z) = 3x2z + 3y2z - 2z3
(a)
To be given during the class
How much work must be done to move a charge
of -2 C from the origin to position (1, 2, 3)?
Answer:
(c)
(x, y, z in metres)
Find the electric field E(x,y,z).
Answer:
(b)
Volts
W = + 18 Joules
[ Think carefully about the sign of W ]
Show that, in any plane parallel to the x-y plane, the
equipotentials are circles centred on the origin.
[What’s the equation of a circle with centre at (0,0)?]