If the electrical potential in a region is constant, the electric field must be zero everywhere in that region.

True
False

False

False.

To determine whether the statement is true or false, we need to understand the relationship between electrical potential and electric field.

The electrical potential, often referred to as voltage, measures the electric potential energy per unit charge at a specific point in a region. It is a scalar quantity and its gradient gives the electric field. The electric field, on the other hand, measures the force experienced by a positive test charge per unit charge at a specific point in a region. It is a vector quantity.

If the electrical potential is constant in a given region, it means that the electric potential energy per unit charge is the same throughout that region. However, this does not necessarily imply that the electric field is zero everywhere in that region.

To confirm whether the statement is true or false, we need to recall the relation between electric field and electric potential. The electric field is the negative gradient of the electric potential, which means that the electric field points towards decreasing electric potential. If the electric potential is constant, the gradient is zero, and hence the electric field is zero.

So, in conclusion, if the electrical potential is constant in a region, the electric field will be zero everywhere in that region. Therefore, the statement is true.

False. Any wire carrying current has an

electric field around it.