The electric potential in a region of space is given by The x-component of the electric field in this region is
A)(10 V/m)
B)-(10 V/m)
C)(20 V/m)
D)-(20 V/m)
E)-(30 V/m)

Question

The electric potential in a region of space is given by  The x-component of the electric field in this region is
A)(10 V/m) 
B)-(10 V/m) 
C)(20 V/m) 
D)-(20 V/m) 
E)-(30 V/m)

Quizplus · Accepted Answer

The x-component of the electric field, Ex, is given by the negative of the partial derivative of the electric potential with respect to x: 
Ex = - (∂V/∂x)

Taking the partial derivative of the given electric potential with respect to x, we get:

∂V/∂x = -10x

Thus, Ex = -(-10x) = 10x

Since we are only interested in the x-component of the electric field, we can ignore the other terms in the electric potential. Therefore, the answer is (B) -(10 V/m).

The Electric Potential in a Region of Space Is Given