Q1 (a) The charge Q on a conductor at time t is given by
Q=Q_o (1-e^(-t⁄T) )
Where Q_o and T are constants.
Find the current I at any time t and [3]
Sketch the variations of I and Q with time [5]
(b) A charge with uniform line density λ is distributed along a thin rod of total length L.
(i) Find the force that this distribution exerts on a point charge Q placed at a point P a distance a on a perpendicular bisector as in figure 1 [10]
Show that when the rod is very short ( i.e. L→0) the distribution behaves like a point charge λL and that
When the rod is very long (i.e. L→∞) then the force is given by the expression [4]
F=Qλ⁄((2πε_o a))
(c) The potential in a region varies along the x-axis according to the equation
V=-kx^3
Where k is a constant. Find the expression for the variation of the electric field along the same axis. [3]
