(a) How strong is the attractive force between a glass rod with a $\mathbf{0}\mathbf{.}\mathbf{700}\mathbf{}\mathit{\mu }\mathit{C}$charge and a silk cloth with a $\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{600}\mathbf{}\mathit{\mu }\mathit{C}$charge, which are 12.0 cm apart, using the approximation that they act like point charges? (b) Discuss how the answer to this problem might be affected if the charges are distributed over some area and do not act like point charges.

• Charge on the glass rod$\left|q_1\right|=0.700\mu C$
• Charge on silk cloth$\left|q_2\right|=-0.600\mu C$

• Separation between rod and cloth$=12.0cm$

When two-point charges are separated by some distance, the Coulomb force is given as,

$F=\frac{K\left|q_1\right|\left|q_2\right|}{r^2}$

Here, K is the electrostatic force constant, $\left|q_1\right|$and $\left|q_2\right|$are the magnitude of charges, and ris the separation between the charges.

The attractive force between the glass rod and silk cloth is,

$F=\frac{K\left|q_1\right|\left|q_2\right|}{r^2}$

Here, K is the electrostatic force constant $\left(K=9\times {10}^{9}N-m^2/C^2\right)$, $\left|q_1\right|$is the magnitude of charge on glass rod $\left(\left|q_1\right|=0.700\mu C\right)$, $\left|q_2\right|$is the magnitude of charge on the silk cloth $\left(\left|q_2\right|=0.600\mu C\right)$ and r is the separation between the glass rod and silk cloth (r = 12.0 cm) .

Substituting all known values,

$$\begin{gathered} F=\frac{\left(9\times {10}^{9}N-m^2/C^2\right)\times \left(0.700\mu C\right)\times \left(0.600\mu C\right)}{{\left(12.0cm\right)}^2} \\ =\frac{\left(9\times {10}^{9}N-m^2/C^2\right)\times \left(0.700\mu C\right)\times \left({\displaystyle \frac{{10}^{-6}C}{1\mu C}}\right)\times \left(0.600\mu C\right)\times \left({\displaystyle \frac{{10}^{-6}C}{1\mu C}}\right)}{{\left[\left(12.0cm\right)\times \left({\displaystyle \frac{1m}{100cm}}\right)\right]}^{-2}} \\ =0.262N \end{gathered}$$

Hence, the force of attraction between the glass rod and the silk cloth is 0.262 N .

If the charges are distributed over some area, the resultant force between the glass rod and the silk cloth will be the vector sum of each force on each pair of charge. Hence, the things would get complicated.

Thus the glass rod and silk cloth will experience a force of 0.262 N between them.