In many cases, we simplify problems involving potentials by assuming V = 0 at in

Question

In many cases, we simplify problems involving potentials by assuming V = 0 at infinity. When are we allowed to make this simplification? (a) The total charge is finite. (b) The total charge is infinite. (c) Both (a) and (b) allow the simplification. Consider a point charge q = 1.5 nC at the origin, and a spherical shell of charge with surface charge density alpha =-0.2 nC/m^2 and radius r = 0.892 m. (a) What is the electric field (magnitude and direction) at a distance of 0.5 m from the origin? (b) What is the electric field (magnitude and direction) at a distance of 1.5 m from the origin?

Explanation / Answer

1) V = k Q / r

at r -> infinity

V= 0

that means Q is finite.

Ans(a)

2) (a) E = k q / r^2

E = (9 x 10^9) (1.5 x 10^-9) / 0.5^2

E = 54 N/C

Direction -> radially away from center

(b) now total charge inside this region,

Q = (1.5 nC) + (- 0.2 ( 4 x pi x 0.892^2)) = - 0.5

E = k Q / r^2 = (9 x 10^9) (0.5 x 10^-9) / 1.5^2

E = 2 N/C

Direction -> radially inward

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