The magnitude of the electric field E of a spherically symmetric charge distribution varies with the distance r from its centre. The graph of E versus r shows that E increases linearly from zero at r=0 to a maximum value E₀ at r=R , and then decreases for r > R . A point charge q is moved slowly from the centre ( r=0 ) to the surface ( r=R ) along a random curved path. What is the magnitude of the work done by the ex

Step-by-step solution

The electrostatic field is conservative, meaning the work done in moving a charge is independent of the path taken and depends only on the initial and final positions. The work done by an external agent in moving a charge q slowly is given by W = q V , where V is the potential difference between the final and initial points. The magnitude of the potential difference | V| between r=0 and r=R is equal to the magnitude of the line integral of the electric field, which corresponds to the area under the E versus r graph