A metal sphere with radius r a = 1.30 cm is supported on an insulating stand at

Question

A metal sphere with radius ra = 1.30 cm is supported on an insulating stand at the center of a hollow, metal, spherical shell with radius rb = 9.90 cm . Charge +q is put on the inner sphere and charge q on the outer spherical shell. The magnitude of q is chosen to make the potential difference between the spheres 420 V , with the inner sphere at higher potential.

Part A

Calculate q.

Part B

Are the electric field lines and equipotential surfaces mutually perpendicular?

Are the electric field lines and equipotential surfaces mutually perpendicular?

No

Part C

Are the equipotential surfaces closer together when the magnitude of E  is largest?

Yes

No

Part C

Are the equipotential surfaces closer together when the magnitude of E  is largest?

Equipotential surfaces closer together when the magnitude of E  is largest. Equipotential surfaces closer together when the magnitude of E  is smallest.

Explanation / Answer

A)

Capacitance of spherical capaciotr, C = 4*pi*epsilon/(1/a - 1/b)

= 4*pi*8.854*10^-12/(1/0.013 - 1/0.099)

= 1.67*10^-12 F

Apply, q = C*delta_V

= 1.67*10^-12*420

= 7.01*10^-10 C or 0.701 nC

B) Yes.

Beacuse, workdone by electric field on equipotential is zero. It means E is peprendicular to the equipotential surface.

C) Equipotential surfaces closer together when the magnitude of E is largest.

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