Question

A sheet of charge with surface charge density 40 nC/m² on the plane. Calculate the work done (in joules) in moving a 10C charge from A(3.3,-1) to B(1,0,-4), all dimensions given in meters. Give your answer

Answer 1

To calculate the work done in moving a charge from point A to point B, we need to find the electric potential energy at both points and subtract them.

Step-by-step explanation:

To calculate the work done in moving a charge from point A to point B, we need to find the electric potential energy at both points and subtract them. The electric potential energy of a point charge is given by U = qV, where q is the charge and V is the electric potential.

First, let's calculate the electric potential at point A:

V_A = kσ / r_A, where k is the electrostatic constant (9 x 10^9 Nm²/C²), σ is the surface charge density (40 nC/m²), and r_A is the distance from point A to the sheet of charge.

Now, let's calculate the electric potential at point B:

V_B = kσ / r_B, where r_B is the distance from point B to the sheet of charge.

The work done is then given by W = q(V_B - V_A), where q is the charge being moved. Plugging in the values and doing the calculations, we can find the work done in joules.