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A point charge +q is placed at a distance d from the centre of an uncharged (neutral) solid metallic cube of side a. What is the electric field at the CENTRE of the cube due only to the induced charges on the cube?

1. q/(4*pi*epsilon0*d²), directed away from +q (toward -y)
2. zero
3. q/(4*pi*epsilon0*d²), directed toward +q
4. q/(4*pi*epsilon0*(d - a/2)²), directed away from +q

Correct answer: q/(4*pi*epsilon0*d²), directed away from +q (toward -y)

Solution

Inside the body of a conductor the net electrostatic field is zero everywhere. The net field at the centre is the superposition of the external point charge's field and the induced-charge field. Setting the total to zero, the induced-charge field at the centre must be exactly equal and opposite to the field of +q there. The external charge produces E = q/(4*pi*epsilon0*d²) pointing away from +q at the centre; therefore the induced charges produce a field of the same magnitude pointing toward +q so they cancel. Magnitude = q/(4*pi*epsilon0*d²).

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