PhysicsLAB AP Free Response Question
2001 C1 E&M

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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.

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