Question

A small sphere of charge +6×10^-6 C is suspended by a string of negligible mass. A charge of -9.0×10^-6 C is placed directly to the right of the sphere and 0.22m away from it. The string is deflected 5^0 from the vertical. Find the tension in the string.

Answer 1

Explanations & Calculations

• The force between the two forces according to Coulomb's law is

$\qquad\qquad \begin{aligned} \small |F|&=\small k\frac{Qq}{r^2}\\ &=\small (8.98\times10^9).\frac{9\times10^{-6}\times6\times10^{-6}}{0.22^2}\\ &=\small 10.01\,N \end{aligned}$

• Since the thread is angled, the horizontal component of tension can be written as follows and the tension can be calculated.

$\qquad\qquad \begin{aligned} \small T\sin\theta&=\small F\\ \small T&=\small \frac{10.01\,N}{\sin5}\\ &=\small 114.85\,N \end{aligned}$