1. A pair of thick conducting slabs are fixed in place near one other as shown, with their faces parallel. The faces have area A, which we will take to be very large compared to the slabs' separation. Initially the slabs are neutral, but then a net charge of +5 C is placed on the left slab, and a net charge of +3 C is placed on the right slab. When things have settled down, some amount of charge has migrated to the outer faces of the slabs, and some amount of charge has migrated to the inner faces of the slabs. This situation is diagrammed below. +5 C +3 C +5C +3C Q5-Q, 3-Q Q WS E4 (rev. 3.0) Page 65 Notice that the charges on the left slab add up to +5 C as required by charge conservation- and likewise for the right slab. Notice also that, in accordance with the rules for conductors, all charges reside on the surfaces of the conductors. The goal of this question will be to use other rules for conductors to determine the unknown charges Q1 and Q2. c) Repeat parts (a) and (b) for the right slab, in order to find Q2. d) What are the charges on the inner surfaces of the slabs? e) You should have found that the charges on the inner surfaces of the slabs are equal and opposite. This will be true regardless of how much charge is on either slab. Can you prove this by drawing an appropriate Gaussian surface and making use of the fact that the field in either slab vanishes? • Treating Qi and Q2 as known quantities, use superposition to find an expression for the electric field within the left slab. b) Taking into account the fact that the slab is a conductor use this expression to find Q.

1. A pair of thick conducting slabs are fixed in place near one other as shown, with their faces parallel. The faces have area A, which we will take to be very large compared to the slabs' separation. Initially the slabs are neutral, but then a net charge of +5 C is placed on the left slab, and a net charge of +3 C is placed on the right slab. When things have settled down, some amount of charge has migrated to the outer faces of the slabs, and some amount of charge has migrated to the inner faces of the slabs. This situation is diagrammed below. +5 C +3 C +5C +3C Q5-Q, 3-Q Q WS E4 (rev. 3.0) Page 65 Notice that the charges on the left slab add up to +5 C as required by charge conservation- and likewise for the right slab. Notice also that, in accordance with the rules for conductors, all charges reside on the surfaces of the conductors. The goal of this question will be to use other rules for conductors to determine the unknown charges Q1 and Q2. c) Repeat parts (a) and (b) for the right slab, in order to find Q2. d) What are the charges on the inner surfaces of the slabs? e) You should have found that the charges on the inner surfaces of the slabs are equal and opposite. This will be true regardless of how much charge is on either slab. Can you prove this by drawing an appropriate Gaussian surface and making use of the fact that the field in either slab vanishes? • Treating Qi and Q2 as known quantities, use superposition to find an expression for the electric field within the left slab. b) Taking into account the fact that the slab is a conductor use this expression to find Q.