Two tiny metal spheres are fixed to the ends of a non-conducting string of length $\ell$ .Equal charges,+q,are placed on the metal spheres.Randall says that the force on the string has magnitude $\frac { 1 } { 2 \pi \varepsilon _ { 0 } } \frac { q ^ { 2 } } { \ell ^ { 2 } }$ .Tilden says that the tension in the string has magnitude $\frac { 1 } { 2 \pi \varepsilon _ { 0 } } \frac { q ^ { 2 } } { \ell ^ { 2 } }$ .Which one,if either,is correct?
A)Randall,because both charges exert forces on the string,but the tension is $\frac { 1 } { 4 \pi \varepsilon _ { 0 } } \frac { q ^ { 2 } } { \ell ^ { 2 } }$ .
B)Tilden,because both charges exert forces on the string,but the net force is $\frac { 1 } { 4 \pi \varepsilon _ { 0 } } \frac { q ^ { 2 } } { \ell ^ { 2 } }$ .
C)Both are correct,because both charges exert forces on the string.
D)Neither is correct,because both the tension and the force have magnitude $\frac { 1 } { 4 \pi \varepsilon _ { 0 } } \frac { q ^ { 2 } } { \ell ^ { 2 } }$ .
E)Neither is correct,because the tension is $\frac { 1 } { 4 \pi \varepsilon _ { 0 } } \frac { q ^ { 2 } } { \ell ^ { 2 } }$ ,but the net force is 0.

Question

Quizplus · Accepted Answer

The tension in the string is given by Coulomb's law as $\frac { 1 } { 4 \pi \varepsilon _ { 0 } } \frac { q ^ { 2 } } { \ell ^ { 2 } }$, and since the charges are equal and opposite, the net force on the string is 0.

Two Tiny Metal Spheres Are Fixed to the Ends of a Non-Conducting