All Problems

Conductors and Dielectrics in an Electric Field

Problem 3.67

Two infinite conducting plates 1 and 2 are separated by a distance \(l .\) A point charge \(q\) is located between the plates at a distance \(x\) from plate \(1 .\) Find the charges induced on each plate.

Reveal Answer
q1=−q(l−x)/l,q2=−qx/l. Instruction. If the charge q is imagined to be uniformly spread over the plane passing through that charge and parallel to the plates, the charges q l and q 2 remain, obviously, unchanged. What changes is only their distribution, and the electric field becomes easy to calculate.q_{1}=-q(l-x) / l, q_{2}=-q x / l . \text { Instruction. If the charge q is imagined to be uniformly spread over the plane passing through that charge and parallel to the plates, the charges q l and q 2 remain, obviously, unchanged. What changes is only their distribution, and the electric field becomes easy to calculate.}
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