Question

A point charge of magnitude +1μ is fixed at (0,0,0).An isolated uncharged spherical conductor is fixed with the center at (4,0,0) Then calculate the potential nd the induced electric field at the centre of the sphere. ​

Answer 1

Here is your answer mate in the attachment hope it help ✌️

Answer 2

The potential and the induced electric field at the centre of the sphere is $\bold{2.25\times10^{5} \ V}$ and $\bold{5.625\times 10^{6} \ V/m}$

Given:

Charge = +1μC $\bold{=1\times10^{-6} \ C}$

Position of the point charge = (0,0,0)

Position of the spherical conductor = (4,0,0)

To find:

Electric potential = ?

induced electric field = ?

Formula used:

Electric potential:

$\bold{V=\frac{kq}{r}}$

induced electric field:

$\bold{E=\frac{kq}{r^2}}$

Where,

k = Electric constant

q = Charge

r = Distance

Solution:

Electric potential:

The conductor is placed in z axis and its distance from the origin is 4. So, r is 4 cm.

$\bold{V=\frac{9\times 10^{9}\times 1\times 10^{-6}}{4\times 10^{-2}}}$

$\bold{\therefore V=2.25\times10^{5} \ V}$

induced electric field:

The conductor is placed in z axis and its distance from the origin is 4. So, r is 4 cm.

$\bold{E=\frac{9\times10^{9}\times1\times10^{-6}}{(4\times10^-2)^2}}$

$\bold{E=\frac{9\times10^9\times1\times10^{-6}}{16\times10^{-4}}}$

$\bold{\therefore E = 5.625\times 10^{6} \ V/m}$