Question

The emf of a particular flashlight battery is 1.7 V. If the battery is 4.5 cm long and radius of cylindrical battery is 1 cm, estimate roughly the amount of charge on the positive end plate of the battery.

Short answer

The amount of charge on the positive end of the battery plate is$1.051\times {10}^{-13}\text{C}$

Step-by-step solution

Identification of given data

The emf of the flashlight battery is $\epsilon =1.7\text{V}$

The length of battery is $l=4.5\text{cm}$

The radius of cylindrical battery is$r=1\text{cm}$

The amount of charge at the positive end of battery plate is found by the product of the capacitance and emf of the battery.

Determination of formula for amount of charge on the positive end of battery plate

The capacitance of the cylindrical battery is given as:$C=\frac{{\epsilon }_0\left(\pi r^2\right)}{l}$

Here, ${\epsilon }_0$is the permeability of free space and its value is$8.854\times {10}^{-12}{\text{C}}^2/\text{N}·{\text{m}}^2$ .

Determination of amount of charge on the positive end of battery plate

Substitute all the values in above equation.

$$\begin{gathered} C=\frac{\left(8.854\times {10}^{-12}{\text{C}}^2/\text{N}·{\text{m}}^2\right)\left[\pi {\left(\left(1\text{cm}\right)\left(\frac{1\text{m}}{100\text{cm}}\right)\right)}^2\right]}{\left(4.5\text{cm}\right)\left(\frac{1\text{m}}{100\text{cm}}\right)} \\ C=6.18\times {10}^{-14}\text{F} \end{gathered}$$

The amount of charge on the positive end of the battery plate is given as:

$q=C\epsilon$

Substitute all the values in above equation.

$$\begin{gathered} q=\left(6.18\times {10}^{-14}\text{F}\right)\left(1.7\text{V}\right) \\ q=1.051\times {10}^{-13}\text{C} \end{gathered}$$

Therefore, the amount of charge on the positive end of the battery plate is$1.051\times {10}^{-13}\text{C}$