Answer to Question #95658 in Electricity and Magnetism for hamza

Question

A charged particle P is situated in a vacuum at a distance x from the centre of a charged
conducting sphere of radius r, as illustrated in Fig. 5.1.
For the particle P outside the conducting sphere, the charge on the sphere may be assumed to
be a point charge at its centre.
a) State Coulomb’s law.
b) The sphere and the particle P are both charged positively.
1. State the direction of the force acting on particle P.
2. State the position of particle P for the force to be maximum.
3. Determine the ratio:
force on particle P at x = r
force on particle P at x = 4r

Answer 1

a) In this case, the Coulomb law looks like:

$f = \frac{kqQ}{x^2}$

q and Q are particle and sphere charges.

b1) force acts in the direction "from the sphere"

b2) the force is maximum when the particle is on the surface of the sphere

b3) the ratio is $(\frac{4r}{r})^2 = 16$