Spheres of charge: A sphere with radius 2.0 mm carries +1.0 μC of charge distributed uniformly throughout its volume. What is the potential difference, V_B - V_A, between point B, which is 4.0 m from the center of the sphere, and point A, which is 9.0 m from the center of the sphere? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Question

Quizplus · Accepted Answer

The potential difference between two points in an electric field is given by the equation:V_B - V_A = -∫_A^B E · dlwhere E is the electric field and dl is the differential displacement vector.For a point charge, the electric field is given by:E = kq/r²where k is Coulomb's constant, q is the charge, and r is the distance from the charge.In this case, the charge is distributed uniformly throughout the volume of the sphere, so the electric field is the same at all points outside the sphere.Therefore, the potential difference between point B and point A is:V_B - V_A = -∫_A^B kq/r² · dl= -kq∫_A^B 1/r² · dl= -kq(1/r_B - 1/r_A)= -(8.99 × 10⁹ N ∙ m²/C²)(1.0 × 10^-6 C)(1/4.0 m - 1/9.0 m)= -1200 VTherefore, the correct answer is A.

Spheres of Charge: a Sphere with Radius 2