Chapter 17, Problem 73GP

To determine

The charge on each coin.

Answer to Problem 73GP

  $2.5\times {10}^{-10}C$

Explanation of Solution

Given data:

Diameter of coin, $D=1.1cm$

Thickness of paper, $d=0.15mm=0.15\times {10}^{-3}m$

Dielectric constant, $K=3.7$

Voltage across the capacitor, $\Delta V=12V$

Formula used:

  $Q=CV$ .

Where,

  $C$ is the capacitance of a capacitor.

  $\text{V}$ is the magnitude of the change in potential across the capacitor.

  $Q$ is magnitude of charge on each plate of the capacitor.

Calculation:

Use the formula $Q=CV$ to find the charge on each coin.

  $Q=CV=K\frac{{\text{ε}}_{0}A}{d}V\mathrm{...}\left(1\right)$

Where,

  $A$ is the area.

  $V$ is the potential.

  ${\text{ε}}_{\text{0}}$ is the permittivity of free space.

  $K$ is dielectric constant

Substitute the all the values in equation $\left(1\right)$

  $\begin{array}{l}=\left(3.7\right)\left(8.85\times {10}^{-12}{C}^2/N\cdot m^2\right)\frac{\pi {\left(0.55\times {10}^{-2}m\right)}^2}{\left(0.15\times {10}^{-3}m\right)}\left(12V\right)\\ =2.5\times {10}^{-10}C\end{array}$

Conclusion:

The required value is $2.5\times {10}^{-10}C$ .