91影视

The given data can be listed below as:

The charge in the middle of the arrangement is \({\rm{q}}\).

The charges at the corner of the arrangement are \({{\rm{q}}_{\rm{a}}}\), \({{\rm{q}}_{\rm{b}}}\), \({{\rm{q}}_{\rm{c}}}\) and \({{\rm{q}}_{\rm{d}}}\) respectively.

The electric field is mainly referred to as a region that helps an electrically charged particle to exert force on another particle. The electric field cannot be created without an electrically charged particle.

If the charges are equal and the distance of all the corner charges to the midpoint is the same, then the magnitude of the charges will also be equal. The direction of the electric field either goes away to comes towards to center of the square.

The electric field of the charge \({{\rm{q}}_{\rm{a}}}\) will point towards the charge \({{\rm{q}}_{\rm{d}}}\) and also the diagonal that connects them and also vice versa. That shows that the net electric field along the \({{\rm{q}}_{\rm{a}}} - {{\rm{q}}_{\rm{d}}}\) diagonal will be zero as the electric field significantly does not influence another charge. The electric field will also be the same along the \({{\rm{q}}_{\rm{b}}} - {{\rm{q}}_{\rm{d}}}\) diagonal. Here, if the sign of the charges also changes, then also the combined electric field will be zero for all the charges.

Thus, the electric field at the center of the square is zero as the magnitude of the electric field of all the charges is equal.

In the above part, the charges are not needed to be the same, only the diagonal charges needed to be the same such as \({{\rm{q}}_{\rm{b}}} = {{\rm{q}}_{\rm{c}}}\) and \({{\rm{q}}_{\rm{a}}} = {{\rm{q}}_{\rm{b}}}\). The reason for this is that the electric field at the diagonal and at the center point is perpendicular, hence the fields are interdependent. Only the electric field of \({{\rm{q}}_{\rm{a}}}\) can be canceled by the electric field of \({{\rm{q}}_{\rm{d}}}\) and vice versa and the same goes for \({{\rm{q}}_{\rm{b}}}\) and \({{\rm{q}}_{\rm{c}}}\).

Thus, for the combination of charges such as \({{\rm{q}}_{\rm{b}}} = {{\rm{q}}_{\rm{c}}}\) and \({{\rm{q}}_{\rm{a}}} = {{\rm{q}}_{\rm{b}}}\), the electric field will also be zero.