A positive charge of 1.6×10 -9 C is brought in from infinity to a point (2m,0).

ID: 1484427 • Letter: A

Question

A positive charge of 1.6×10-9 C is brought in from infinity to a point (2m,0).

How much work did the electric field do?

W =

0 J

Please help with parts 2 and 3

2)Now another positive charge of 1.6×10-9 C is moved from infinity to the coordinates (1m, 2m).

How much additional work was done by the electric field? (The original charge is held in place.)

W =

____________J

3)Finally, a negative charge of -1.6×10-9 C is moved from infinity to the coordinates (-2m,0).

How much additional work was done by the electric field? (The original two charges is held in place.)

W =

____________J

2)
work done = -change in potential energy
= -(Ubefore - U after)
= -(K*q1*q1/r - 0 )
= -K*q1*q1/r

r = (1,2) - (2,0) = (-1,2) = sqrt (1^2 + 2^2) = sqrt (5) = 2.236 m

work done = -K*q1*q1/r
= - (9*10^9)*(1.6*10^-19)*(1.6*10^-19) / (2.236)
= -1.03*10^-28 J

c)
work done = - potential energy of -e charge
= -K*(q1/r1 + q2/r2)*e

r1 = 4 m
r1 = (-2,0) - (1,2) = (-3,-2) = sqrt (3^2 + 2^2) =3.6 m

work done = -K*(q1/r1 + q2/r2)*e
= -(9*10^9)*((1.6*10^-19)/4 + (1.6*10^-19)/3.6)* (-1.6*10^-19)
= 1.22*10^-28 J

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