Question

The potential at the centre of uniformly charged circular disk of radius R=3.5cm is V.=550v. what is the total charge on disk.​

Answer 1

Given:

The potential at the centre of uniformly charged circular disk of radius R=3.5cm is V=550 volts.

To find:

Total charge on disc?

Calculation:

General expression for Electrostatic potential on axis of disc is (x is distance from centre):

$\boxed{ \bf \: V = \dfrac{q}{2\pi \epsilon_{0} {r}^{2} } \bigg \{ \sqrt{ {x}^{2} + {r}^{2}} - {x}^{2} \bigg \}}$

For centre , x = 0.

$\boxed{ \bf \: V = \dfrac{q}{2\pi \epsilon_{0}r} }$

Putting necessary values:

$\rm \implies V = \dfrac{2q}{4\pi \epsilon_{0}r}$

$\rm \implies 550 = \dfrac{2q}{ (\frac{3.5}{100} )} \times (9 \times {10}^{9} )$

$\rm \implies 275= \dfrac{100q}{3.5} \times (9 \times {10}^{9} )$

$\rm \implies \: q = \dfrac{275 \times 3.5}{9 \times {10}^{11} }$

$\rm \implies \: q = 106.9 \times {10}^{ - 11}$

$\rm \implies \: q = 1.07 \times {10}^{ - 9} \: C$

$\rm \implies \: q = 1.07 \: nC$

So, charge on disc is 1.07 nC.