Charge is placed on two conducting spheres that are very far apart and connected by a long thin wire. The radius of the smaller sphere is 5 cm and that of the larger sphere is 12 cm. The electric field at the surface of the larger sphere is 280 kV/m. Find the surface charge density on each sphere.

1.02*10^-5 C/m²

Explanation:

Given that

Radius of the smaller sphere, r = 0.05 m

Radius of the larger sphere, R = 0.12 m

Electric field, E = 2*10^5 V/m

Formula for the electric field is

E = Q / (4πεR²)

this then means that the surface charge density of the larger sphere is

Q/4πR² = Eε = 1.77*10^-6 C/m²

and

Q = 4πεER² = 3.203*10^-7 C

is the charge on the large sphere, which is the same as the charge on the small sphere since they are connected by the wire

so the surface charge density of the smaller sphere is

Q/4πr² = 4πεER²/4πr²

Q = εER²/r²

Q = 1.02*10^-5 C/m²