Since the charge is being moved perpendicular to the direction of electric field between the plates the work done should be zero. But the answer is positive(A). Could you please explain the concept behind this?

It's a common point of confusion when dealing with electric fields and the movement of charges. Let's break down the situation you're describing to clarify why the work done is positive even when the charge moves perpendicular to the electric field.

Understanding Electric Fields and Work

First, it's essential to grasp what an electric field is. An electric field is a region around a charged object where other charged objects experience a force. The direction of the electric field is defined as the direction a positive test charge would move. When a charge moves within this field, work can be done on or by the charge, depending on the direction of movement relative to the field.

Work Done by Electric Forces

The work done (W) on a charge (q) in an electric field (E) can be calculated using the formula:

• W = qEd

Here, d is the displacement of the charge in the direction of the electric field. If the charge moves in the same direction as the field, the work done is positive. If it moves against the field, the work done is negative. If the movement is perpendicular to the field, intuitively, one might think that no work is done, as there is no displacement in the direction of the field.

Perpendicular Movement and Potential Energy

However, when a charge moves perpendicular to the electric field, it does not mean that no work is done in the context of energy transfer. Instead, the charge may be moving in a way that changes its potential energy. For instance, if a charge moves from one plate of a capacitor to another, even if it moves sideways (perpendicular to the field), it can still gain kinetic energy or change its potential energy due to the configuration of the electric field.

Example of a Capacitor

Consider a parallel plate capacitor. The electric field between the plates is uniform and directed from the positive plate to the negative plate. If you move a positive charge from the positive plate to a point directly across from it on the negative plate, even if that movement is sideways, the charge is still influenced by the electric field. The work done by the electric field on the charge is related to the potential difference between the plates.

In this case, the charge gains energy as it moves through the electric field, which can be seen as positive work being done on the charge. The energy gained can be thought of as the charge moving to a position of higher potential energy, even if its path was not directly along the field lines.

Conclusion

In summary, while it might seem that moving a charge perpendicular to an electric field would result in zero work done, the reality is that the context of the electric field and the potential energy changes must be considered. The work done is indeed positive because the charge is still influenced by the electric field, leading to changes in energy. This concept is crucial in understanding how electric fields operate and the behavior of charges within them.