Question

A metallic sphere has a charge of 10 microcolumb. A UNUT NEGATUVE CHARGE IS BROUGHT FROm A to B both 100 cm away from sphere but A being east of it while B being on west The net workdone is

Answer 1

The work done is, W = 0

Step-by-step explanation:

Given,

The charge of the metallic sphere, Q = 10 μ C

The charge of the test charge, q = -1

The initial position of the unit charge, A = 100 cm

The final position of the unit charge, B = 100 cm

The work done by the unit charge is given by the equation

`W=V=\int\limits^A_B{F}\, dx`

Where F is the force between two charges

`F=(1)/(4\pi\epsilon_(0)) (QX(-1))/(x^(2))`

`F=-(1)/(4\pi\epsilon_(0)) (Q)/(x^(2))`

Substituting in the above equation

`W=V=-\int\limits^A_B{(1)/(4\pi\epsilon_(0)) (Q)/(x^(2))} \, dx`

On integrating for the limit A to B

`V=[(Q)/(4\pi\epsilon_(0)x)]^(B) _(A)`

Substituting the integral values

`V=(10)/(4\pi\epsilon_(0)(1))-(10)/(4\pi\epsilon_(0)(1))`

V = 0

The work done by a unit charge on an electric field from A to B is the difference between the electric potential of the two locations. If the locations are at the same distance from the origin, the work done will be zero.

Hence, the work done by moving a unit negative charge from point A to B is, V = 0