Consider the situation shown in the Figure. The charges shown are q 1 = 2.0 ?C (
ID: 2290544 • Letter: C
Question
Consider the situation shown in the Figure. The charges shown are q1 = 2.0 ?C (bottom left charge), and q2 = 6.0 ?C. Charge q3 = -2.0 ?C (not shown) is at infiniti. The distances are a =1.50cm, b =3.90cm, and c =2.50cm. The point labeled "X" is at the top left corner, a distance c away from q1 and a distance a away from the point labeled Y. The point labeled "Y" is between charges q1 and q2, it is a distance a away from q1 and a distance b away from q2.
(a) With charges q1 and q2 in place, how much additional energy in Joules needs to be expanded to bring charge q3 to the point labeled "Y"?
(b) With charges q1 and q2 in place, how much additional energy in Joules needs to be expanded to instead bring charge q3 to the point labeled "X"?
(c) What if q3 was already brought to "X" how much energy in Joules needs to be expanded to move it to the point labeled "Y"?
MUST SHOW FULL WORK WITH NUMBERS
Explanation / Answer
a) potentaial at point, Y
Vy = k*q1/a + k*q2/b
= 9*10^9*2*10^-6/0.015 + 9*10^9*6*10^-6/0.039
= 2.584*10^6 volts
Workdone = q3*(Vy - 0)
= -2*10^-6*(2.584*10^6 - 0)
= -5.17 J
b) potentaial at point, X
Vx = k*q1/c + k*q2/sqrt((a+b)^2 + c^2)
= 9*10^9*2*10^-6/0.025 + 9*10^9*6*10^-6/sqrt((0.015+0.039)^2+0.025^2)
= 1.627*10^6 volts
Workdone = q3*(Vx - 0)
= -2*10^-6*(1.627*10^6 - 0)
= -3.25 J
C)
Workdone to move the charge from X to Y,
W = q3*(Vy-Vx)
= -2*10^-6*(2.584*10^6 - 1.627*10^6)
= -1.914 J