Question

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

Answer 1

Answer:

Explanation:

q1= q2= q

F=103N

r=10 cm = 0.1 m

K= 5

F= q^2/4πE° r^2

q^2= 103× 5×(0.1)^2 / 9×10^9

q^2 = 5.15/ 9×10^9

q= √0.572×10^-9

q = 23.9× 10^-6C

Answer 2

Answer:

Charge on each sphere is $Q=2.41\times 10^{-5} C$.

Explanation:

Given that two metal spheres having equal charges of same polarity repel each other with a force of 103N when they are at a distance of 10cm and are in a medium of dielectric constant 5.

Force on the spheres are given by,

$F=\frac{KQ_{1} Q_{2} }{r^{2} } =\frac{Q^{2} }{4\pi E_{r}\times r^{2} } =103N\\\frac{Q^{2} }{4\pi E_{0} \times 5\times(0.1)^{2} } =103N$

On solving $Q=2.41\times 10^{-5} C$

Hence, Charge on each sphere is $Q=2.41\times 10^{-5} C$.