Question

2 identical metal spheres having equal and similar charges repel each other with a force of 103 newton when they are placed 10cm apart in a medium of dielectric constant 5. Determine the charge on each sphere.

Answer 1

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Answer 2

The charge on each sphere is $\bold{74.4 \ \mu C}$

Given:

Force between charges $\bold{=10^3 \ N}$ = F

Distance between charges = 10 cm = 0.1 cm = r

Dielectric constant = 5 = K

To find:

Charge on each sphere = ?

Solution:

$\bold{F_m=\frac{F_{air}}{K}}$

$\bold{F=\frac{1}{K}[\frac{kq1.q2}{r^2}]}$

$\bold{q1.q2=\frac{F.K.r^2}{k}}$

On substituting known values, we get,

$\bold{k = 9 \times 10^9 \ Nm^2/C^2}$

$\bold{q1 = q2 = q}$

Now, the equation becomes,

$\bold{q^2=\frac{1000\times5\times(0.1)^2}{9\times10^9}}$

$\bold{q^2 = 5.55 \times 10^{-9} \ C}$

Thus, the charge on each sphere is:

$\bold{q=74.4 \times10^{-6}\ C = 74.4 \ \mu C}$