PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Electric Force Field and Potential · Electric Force Field and Potential
Problem
Four identical positive point charges, each of magnitude +Q, are fixed at the corners of a square of side length d that lies in vacuum. A thin, flat slab of dielectric material with relative permittivity εr completely fills the right-hand half of the square; the left-hand half remains vacuum. A small positive test charge of magnitude q0 is placed at the geometric center of the square.
(a) With no dielectric present, calculate a symbolic expression for the magnitude of the net electrostatic force on the test charge.
(b) With the dielectric slab in place, only those interactions whose electric-field paths pass entirely through the slab are modified. Write expressions for the individual force vectors exerted on the test charge by each corner charge, clearly indicating which forces are affected by the factor εr. Hence obtain an expression for the net force vector on the test charge in terms of Q, q0, d, εr, and fundamental constants.
(c) Evaluate the magnitude and direction of the net force for Q=2.0μC, q0=0.50μC, d=0.10m, and εr=4. State the direction as an angle measured counter-clockwise from the positive x-axis.