Consider a thin spherical shell of radius R with its centre at the origin, carrying uniform positive surface charge density. The variation of the magnitude of the electric field \(E(r)\) and electric potential \(V(r)\) with the distance r from the centre, is best represented by which graph? Continuous curve stands for intensity. Dotted curve stands for potential.
Show Hint
Inside a uniformly charged shell the field is zero and the potential is constant; outside both fall with distance.
Step 1: Understanding the Concept
For a uniformly charged thin shell, Gauss's law gives zero field inside because no charge is enclosed.
Step 2: Electric field
\(E=0\) for \(r<R\), and for \(r>R\), \(E=\dfrac{kQ}{r^{2}}\), which has its maximum just outside the surface and then falls. So \(E\) jumps from zero at \(r=R\).
Step 3: Potential
Inside, \(E=0\) means \(V\) is constant and equal to the surface value \(\dfrac{kQ}{R}\). Outside, \(V=\dfrac{kQ}{r}\) decreases smoothly.
Step 4: Compare the options
The correct picture has a solid curve at zero up to \(R\) then a jump and decay, and a dotted curve flat up to \(R\) then decaying. This is graph D, option (C).
Final Answer:
Graph D represents the field and potential of the shell, option (C).
\[ \boxed{\text{(C) }\text{Graph D}} \]
