Two identical small charged spheres hang in equilibrium with equal masses as sho

Question

Two identical small charged spheres hang in

equilibrium with equal masses as shown in

the figure. The length of the strings are equal

and the angle (shown in the figure) with the

vertical is identical.

The acceleration of gravity is 9.8 m/s2

and the value of Coulomb’s constant is

8.98755 °x 109 Nm2/C2 .Find the magnitude ofthe charge on each

sphere.

Answer in units of C

Two identical small charged spheres hang in equilibrium with equal masses as shown in the figure. The length of the strings are equal and the angle (shown in the figure) with the vertical is identical. The acceleration of gravity is 9.8 m/s^2 and the value of Coulomb?s constant is 8.98755 x 10^9 Nm2/C2 .Find the magnitude ofthe charge on each sphere. Answer in units of C

Explanation / Answer

Just analyze forces on one sphere: . distance between spheres = 0.08sin3 + 0.08sin3 =   0.00837377 m .          horizontalforces arebalanced:           Tension sin3 = kqq/r2 .          vertical forces arebalanced:              Tension cos3 = mg . divide theequations...                    tan3 = k q2 / mgr2 . Solve for q...     q2 = m g r2 tan3 / k =   0.04 * 9.80 * 0.008373772 * tan3 / 8.99 x109 .      q2 =   1.6024 x10-16       so     q= 1.266 x 10-8 Coulomb . Solve for q...     q2 = m g r2 tan3 / k =   0.04 * 9.80 * 0.008373772 * tan3 / 8.99 x109 .      q2 =   1.6024 x10-16       so     q= 1.266 x 10-8 Coulomb

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