A small, thin, hollow spherical glass shell of radius R carries a uniformly dist

Question

A small, thin, hollow spherical glass shell of radius R carries a uniformly distributed positive charge +Q, as shown in the diagram above. Below it is a horizontal permanent dipole with charges +q and -q separated by a distance s (s is shown greatly enlarged for clarity). The dipole is fixed in position and is not free to rotate. The distance from the center of the glass shell to the center of the dipole is L.

The charge on the thin glass shell is +5e-09 coulombs, the dipole consists of charges of 2e-11 and -2e-11coulombs, the radius of the glass shell is 0.12 m, the distance L is 0.36 m, and the dipole separation is 2e-05 m. Calculate the net electric field at the center of the glass shell. The x axis runs to the right, the y axis runs toward the top of the page, and the z axis runs out of the page, toward you.

If the upper sphere were a solid metal ball with a charge +5e-09 coulombs, what would be the net electric field at its center?

Explanation / Answer

A)

dipole moment, p = q*s

= 2*10^-11*2*10^-5

= 4*10^-16 C.m

E(dipole) = k*p/L^3

= 9*10^9*4*10^-16/(0.36^3)

= 7.72*10^-5 N/c

E(shell) = 0

Enet = E(dipole) + E(shell)

= 7.72*10^-5 N/c <<<<<<<<<<---------------Answer

B) Enet = 0

because in side a metal electric field is always zero.

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