Question

A capacitor is connected to batteries by Nichrome wires and allowed to charge completely. Then the plates are suddenly moved farther apart. Describe what happens and explain in detail why it happens, based on fundamental physical principles. If you give a direction for a current, state whether you are describing electron current or conventional current. Include appropriate diagrams to support your explanation.

Short answer

The spacing between the plates increases, the capacitance reduces, and the current direction is reversed.

Step-by-step solution

Write the given data from the question.

The distance between the plates of the capacitor is increased when capacitor is completely charged.

Determine the formula to describe the given situation.

The capacitance of the capacitor is given by the ratio of the product of area of plates and permeability of space and spacing between the plates.

The expression to calculate the value of the capacitor is given as follows

$\mathit{C}\mathbf{=}\frac{\mathbf{A}{\mathbf{\epsilon }}_{\mathbf{0}}}{\mathbf{d}}$

Here, is the spacing between the plates, is the area of plates and is the permeability of the space.

Describe the given situation.

The initial value of the capacitance is given by,

$C_1=\frac{A{\epsilon }_0}{d_1}$ …… (i)

Here, is the initial distance between the plates.

Consider the circuit given below in which the direction of the conventional current is shown by the arrows.

Let’s assume the plates are separated by the new spacing . The capacitance is given by,

$C_2=\frac{A{\epsilon }_0}{d_2}$ …… (ii)

Here, $d_2$is the new distance between the plates.

From equations (i) and (ii), it is clear that the capacitance is inversely proportional to the spacing between the plates.

The capacitor plates move away, and the distance between plates increases, reducing capacitance. Since in both cases, capacitance is connected with the same voltage, due to which the current flows back to the power supply to restore the voltage.

Therefore, the current starts to flow in the reverse direction, and the arrows show the direction of the conventional current.

Hence when the spacing between the plates is increases the capacitance reduces and direction of the current get reversed.