Question

A conducting sphere of radius R carries a total charge Q. The electric field at a distance r>R from the center is:

• A. kQ/r\(^2\)
• B. kQ/2R\(^2\)
• C. kQ/R
• D. 0

Hint:

This is a key result from Gauss's Law. For a spherical shell or solid conducting sphere: - \textbf{Outside (r>R):} \(E = kQ/r^2\) (acts like a point charge). - \textbf{Inside (r<R):} \(E = 0\) (for a conductor or hollow shell).

Answer 1

The Correct Option is A

Step 1: Apply Gauss's Law for a point external to the sphere. For a spherically symmetric charge distribution, the electric field beyond the distribution (for \(r>R\)) is equivalent to that of a point charge located at the center, encompassing all the charge.
Step 2: State the formula for the electric field of a point charge. The electric field \(E\) at a radial distance \(r\) from a point charge \(Q\) is defined by Coulomb's Law as: \[ E = \frac{kQ}{r^2} \] Here, \(k\) is defined as \(k = \frac{1}{4\pi\epsilon_0}\).
Step 3: Determine the electric field for the sphere. As the point of consideration is outside the conducting sphere, the sphere's total charge \(Q\) can be modeled as a point charge situated at its center. Consequently, the electric field at any distance \(r>R\) is: \[ E = \frac{kQ}{r^2} \]