Question

An electric field is defined along the x-axis by the function E(x) = -3xê . What is V(g)-V(h), where g=3.3m and h=7m?

A.11.1 V
B.- 11.1 V
C.16.33 V
D.-16.33 V
E.73.5 V
F.-73.5 V
G.57.16 V
H.-57.16 V

Answer 1

To find V(g)-V(h), we need to integrate the electric field, E(x), along the x-axis from g to h. Substituting the given electric field function into the integral, we can evaluate and find the potential difference. The correct answer is H. -57.16 V.

Step-by-step explanation:

To find the potential difference, V(g)-V(h), we need to integrate the electric field, E(x), from position g to position h.

V(g)-V(h) = -∫[g to h] E(x) dx

Substituting the formula for the electric field, E(x) = -3xê, we have:

V(g)-V(h) = -∫[g to h] -3x dx

Integrating the expression, we get:

V(g)-V(h) = [3/2 * x^2] evaluated from g to h = 3/2 * (h^2 - g^2)

Substituting g = 3.3m and h = 7m into the equation gives:

V(g)-V(h) = 3/2 * (7^2 - 3.3^2) = 3/2 * (49 - 10.89) = 3/2 * 38.11 = 57.165 V

Therefore, the correct answer is H. -57.16 V.