The next five questions concern the same physical situation. Two charges are pla

Question

The next five questions concern the same physical situation. Two charges are placed 2m apart on a line. How much work was required to assemble these charges from infinitely far apart? 1.3 times 10^-2 J 7.2 times 10^-2 J 3.3 times 10^-2 J -2.7 times 10^-2 J -4.5 times 10^-2 J What direction does the electric field point, at the location 4m to the left of Q1? up left right At what distance from Q_1 along the dotted line is the electric field equal to zero? 0.47 m to the right 1.3 m to the right 0.58 m to the right 1.5 m to the right 3.4 m to the right

Explanation / Answer

1) The work required to assemble these charges is equal to difference in intial and final potential energy of two charges

W = dU = Uf - Ui = kq1*q2/r - kq1*q2/(infinty) =  kq1*q2/r - 0 = 9*109 * (2*10-6)(-5*10-6 )/(2) = -0.045 (option e)

2) The field at a distance 4 m to left from first charge is given by E1 + E2 (where E1 and E2 are fields due to Q1 and Q2 respecitvely)

E1 = kQ1/r2 = 9*109 * (2*10-6)/42 = 1125 N/C (towards left)

E2 = kQ2/r2 = 9*109 * (-5*10-6)/(4+2)2 = - 1250 N/C (towards right)

Hence net field at that point = E1 + E2 = 1125 - 1250 = -125 N/C (toward left) (option b)

3) Let net field is zero at a distance r from Q1

Hence E1 + E2 = 0

kQ1/r2 + kQ2/(r+2)2 = 0

(2*10-6)/r2 - (5*10-6)/(r+2)2 = 0

2/r2 = 5/(r+2)2

r = 3.44 m (option e)

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