Question

The electric potential is given by the functionv (x) = ax bx³. where a and b are constants. compute the electric field.

Answer 1

To find the electric field from the given electric potential V(x) = ax - bx³, differentiate the potential with respect to x and apply a negative sign, resulting in E(x) = -a + 3bx².

Step-by-step explanation:

The electric field E can be computed from the electric potential V(x) by taking the negative gradient (in one dimension, the negative derivative) of the potential function with respect to position x. Given the electric potential function V(x) = ax - bx³, we differentiate this with respect to x to find the electric field:

E(x) = -∂V(x)/∂x = - (d/dx)(ax - bx³) = - (a - 3bx²).

Therefore, the electric field E as a function of position x is E(x) = -a + 3bx².