Electric Potential Question!

Question

A spherical conductor has a radius of 14 cm and a charge of 26 𝜇C. Calculate

the electric field and the electric potential at (a) 𝑟 = 10 cm, (b) 𝑟 = 20 cm, and

(c) 𝑟 = 14 cm from the center.

Answer 1

Let's first talk about Electric field -

At r= 10 cm i.e. inside the conductor, there will be no electric field. Thus, E=0.

At r = 20 cm, the spherical conductor acts as a point charge placed at the centre. Thus E = KQ/r². So, E=9*10⁹*26*10^-6/(0.2²) = 5.85*10⁶ N/C.

At r = 14 cm, again the spherical conductor acts as a point charge located at the centre of the sphere. So E = 9*10⁹*26*10^-6/(0.14²) = 11.9*10⁶ N/C.

Now let's talk about electric potential -

At r = 20 cm, V = KQ/r i.e. V = 9*10⁹*26*10^-6/(0.2) = 1.17*10⁶ N/C-m

At r = 14 cm, V = KQ/r i.e. V = 9*10⁹*26*10^-6/(0.14) = 1.67*10⁶ N/C-m

At r = 10 cm, the potential will be equal to the potential at the surface i.e. 1.67*10⁶ N/C-m.