Question

The electric field in a region of space has the components Ey = Ez = 0 and Ex = (4.00 N/C · m) x. Point A is on the y axis at y = 3.80 m, and Point B is on the x axis at x = 4.40 m. What is the potential difference VB − VA?

Answer 1

`V_(b)-V_(a) = -38.72`

Step-by-step explanation:

Consider the axis diagram attached.

Given:

Ey = Ez = 0

Eₓ = - 4x N/C · m

Since electric field is in x direction, potential difference would be:

`V_(b) - V_(a) =-\int\limits^(4.40)_(0) {E_(x) } \, dx`

Here we integrate between limits 0 and 4.40 which is distance between A and B along x-axis.

`V_(b) - V_(a) = -4 \left[\begin{array}{ccc}(x^(2) )/(2) \end{array}\right]^(4.40)_(0)`

`V_(b)-V_(a) = -4 (9.68)\\V_(b)-V_(a) = -38.72`