A charge Q = -52.1 nC is located L1 = 0.293 m from point A and L2 = 0.450 m from

Question

A charge Q = -52.1 nC is located L1 = 0.293 m from point A and L2 = 0.450 m from point B, as shown in the figure below. What is the potential at A? What is the potential at B? If a point charge q is moved from A to B while Q is fixed in place, through what potential difference does it move? Does its potential increase or decrease? The potential increases. The potential decreases. If q = -1.15 nC, what is the change in electric potential energy as it moves from A to B? Does its potential increase or decrease? The potential energy increases. The potential energy decreases. How much work is done by the electric field due to charge Q as q moves from A to B?

Explanation / Answer

Q=-52*10^-9 C

k=9*10^9

v=k*Q/r

(a) What is the potential at A?

va=9*10^9*(-52*10^-9)/0.293 = -1597.27 V

(b) What is the potential at B?

vb=9*10^9*(-52*10^-9)/0.450 = -1040 V

c)

The potential difference of b with respect to a

vb-va=(-1040)-(-1597.27) = 527.27 v

Since positive work must be done to move the +q test charge

from a to b: it's potential increases

d)

PE=(vb-va)*(-1.15*10^-9)

527.27*(-1.15*10^-9) = -0.0000006063 J

it's potential energy decreases

work done by the field

e)

Since q is positive, the field will not move q from A to B without

and external source of energy:

work = deltav*q= 527.27*q J

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