A conducting sphere 45 cm in diameter carries an excess of charge,and no other charges are present.You measure the potential of the surface of this sphere and find it to be 14 kV relative to infinity. The excess charge on this sphere is closest to
A)0.35 nC.
B)79 nC.
C)315 nC.
D)350 nC.
E)700 nC.

Question

A conducting sphere 45 cm in diameter carries an excess of charge,and no other charges are present.You measure the potential of the surface of this sphere and find it to be 14 kV relative to infinity.  The excess charge on this sphere is closest to
A)0.35 nC. 
B)79 nC. 
C)315 nC. 
D)350 nC. 
E)700 nC.

Quizplus · Accepted Answer

The potential of a conducting sphere is given by:

$$V=\frac{Q}{4\pi \epsilon_0 r}$$

where Q is the total charge on the sphere, r is the radius of the sphere, and $\epsilon_0$ is the permittivity of free space.

We know the diameter of the sphere is 45 cm, so the radius is 22.5 cm or 0.225 m.

We also know the potential of the sphere is 14 kV or 14,000 V.

Substituting these values into the equation above, we can solve for Q:

$$14,000=\frac{Q}{4\pi \epsilon_0 (0.225)}$$

Solving for Q, we get:

$$Q = 3.5 	imes 10^{-7} 	ext{ C or } 350 	ext{ nC}$$

Therefore, the excess charge on the sphere is closest to 350 nC, which is answer choice D.

A Conducting Sphere 45 Cm in Diameter Carries an Excess