The electric field at point P just outside the outersurface of a hollow spherica

Question

The electric field at point P just outside the outersurface of a hollow spherical conductor of inner radius 10 cm andouter radius 20 cm has magnitude 430N/C and is directed outward. When an unknown point chargeQ is introduced into the center of the sphere, theelectric field at P is still directed outward but is now175 N/C. (a) What is the net charge on and enclosed bythe outer spherical surface before Q is introduced?
1 C

(b) What is charge Q?
2 C

(c) After Q is introduced, what is the charge on the innersurface of the conductor?
3 C

(d) What is it on the outer surface?
4 C (a) What is the net charge on and enclosed bythe outer spherical surface before Q is introduced?
1 C

(b) What is charge Q?
2 C

(c) After Q is introduced, what is the charge on the innersurface of the conductor?
3 C

(d) What is it on the outer surface?
4 C

Explanation / Answer

a) Qa = 4 0 R2E since charge within the conductor cannot exert fieldoutside of                    the conductor since the field within the conductor must bezero    Qa = .22 * 430 / 9 * 10E9 =1.911 * 10E-9 C b) after introducting Q     QT= .22 * 175 / 9 * 10E9 = .778 * 10E-9 C    Q = QT - Qa = -1.133 *10E-9 C c) Q induces 1.133 * 10E-9 C on the inner surface d) the charge on the outer surface is .778 * 10E-9 C     (1.133 * 10E9 moved from the outer to innersurface to offset Q)

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