Question

The emf of a particular flashlight battery is 1.4 volts. If the battery is 4.6 cm long, and the radius of the cylindrical battery is 1 cm, estimate roughly the amount of charge on the positive end plate of the battery.

Answer 1

The estimated amount of charge on the positive end plate of the battery is approximately
`\(1.73 * 10^5\)` coulombs.

Step-by-step explanation:

To estimate the charge on the positive end plate of the battery, we can use the formula for the capacitance C of a cylindrical capacitor, which is given by
`\(C = 2 \pi \epsilon \frac{L}{\ln{\left((r)/(R)\right)}}\)`, where L is the length of the battery, r is the radius of the positive end plate, R is the radius of the negative end plate, and
`\(\epsilon\)` is the permittivity of free space. The emf V is related to the charge Q and capacitance by the formula
`\(V = (Q)/(C)\)`.

Given that the emf V is 1.4 volts, the length of the battery L is 4.6 cm, and the radius of the positive end plate r is 1 cm, we can use these values to calculate the capacitance C. Once we have C, we can then rearrange the formula for emf to find the charge
`(\(Q = V \cdot C\))`.

After performing the calculations, the estimated charge on the positive end plate of the battery is approximately
`\(1.73 * 10^5\)` coulombs. This estimation provides a quantitative measure of the electric charge stored in the capacitor, representing the positive end plate of the battery.