The electric field in a region of space is given by Ex = (3.0x) N/C, Ey = Ez = 0, where x is in m. Points A and B are on the x axis at xA = 3.0 m and xB = 5.0 m. Determine the potential difference VB − VA.

Question

Quizplus · Accepted Answer

We can use the formula for potential difference ΔV = Vfinal − Vinitial, where V is the electric potential. The electric potential is the negative of the line integral of the electric field along a path, so we have:

ΔV = ∫A→B (−E·dl)

where A→B represents the path from point A to point B, and dl is a small displacement along the path.

Along the x axis, the electric field only has an x component, so we can simplify the integral to:

ΔV = −∫xA→xB Ex dx

ΔV = −∫3.0 m→5.0 m (3.0x) dx

ΔV = −[1.5x^2]3.0 m5.0 m

ΔV = −(1.5x^2)5.0 m + (1.5x^2)3.0 m

ΔV = −37.5 V + 22.5 V

ΔV = −15 V

Finally, we have to remember that we are looking for VB − VA, so we have:

VB − VA = −ΔV = +15 V

Therefore, the answer is A) −24 V.

The Electric Field in a Region of Space Is Given