The electric field in a region of space is given by the function E = Gamma x^2 x

Question

The electric field in a region of space is given by the function E = Gamma x^2 x where Gamma is a constant with value Gamma = 120 N/C/m^2 Compute the potential difference Delta V_AB between the point A at x = 2m and the point B at x = 4m. Explain how you selected the sign of the potential difference. Consider a spherical volume of charge of outer radius b, inner radius a, and uniform volume charge density rho > 0. Compute the electric potential difference between a point at infinity and the center of the charged sphere.

Explanation / Answer

a] delta V = integral E dx = integral 120* x^2 dx

= 120*[4^3/3 -2^3/3]

= 2240 V

b] Potential difference is always positive as it is difference between two values.

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