An electric potential has the value (22V/m)(y)- (13V/m² )(z-3m)².What is the electric field at the origin?

Question

Quizplus · Accepted Answer

To find the electric field, we need to take the gradient of the electric potential:
E = -∇V
where ∇ is the gradient operator, which consists of the partial derivative with respect to x, y, and z.
In this case, since the electric potential only depends on y and z, we have:

E = - (∂V/∂y)ŷ - (∂V/∂z)ẑ
E = - (22 V/m)ŷ - (-13 V/m)ẑ
E = -22 V/m ŷ + 13 V/m ẑ

Therefore, the correct answer is D, which corresponds to -22V/m ŷ - 78 V/m ẑ when the respective components are multiplied by -1.

An Electric Potential Has the Value (22V/m)(y)- (13V/m2 )(Z-3m)2

An Electric Potential Has the Value (22V/m)(y)- (13V/m² )(Z-3m)²