PhysicsLAB: 2001 C1 E&M

A thundercloud has the charge distribution illustrated below left. Treat this distribution as two point charges, a negative charge -30 C at a height of 2 km above ground and a positive charge +30 C at a height of 3 km. The presence of these charges induces charges in the ground. Assuming the ground is a conductor, it can be shown that the induced charges can be treated as a charge of +30 C at a depth of 2 km below ground and a charge of -30 C at a depth of 3 km, as shown below right.

Consider point P₁, which is just above the ground directly below the thundercloud and point P₂, which is 1 km horizontally away from P₁.

	a. Determine the direction and magnitude of the electric field at point P₁.

b. Regarding the electric field at P₂

	i. On the diagram above, clearly indicate the direction of electric field at point P₂.

	ii. How does the magnitude of the field at this point compare with the magnitude at point P₁? Greater Equal Lesser

c. Letting the zero of potential be at infinity, determine the potential at these points.

	i. Point P₁

	ii. Point P₂

	d. Determine the electrical potential at an altitude of 1 km directly above point P₁.

	e. Determine the total electrical potential energy of this arrangement of charges.