1.) An electric charge q1 = 10 C remains located at the origin of a coordinate s

Question

1.) An electric charge q1 = 10 C remains located at the origin of a coordinate system. A second electrical charge q2 = 20 C is moved from point to point.

(a) How much work is required by an external force to move the second charge along the x-axis from point (1 m, 0) to (2m, 0)?

(b) What is the electric potential at the point (1 m, 0) due to the charge at the origin?

(c) What is the potential difference between the points (1 m, 0) and (2 m, 0)?

(d) What is the potential difference between points (1 m, 0) and (0, 1 m)?

(e) How much work is required by an external force to move the second charge from point (1 m, 0) to (0, 1 m)?

(f) What is the integral E.dl along a circle from point (1 m, 0) to (0, 1 m)?

Explanation / Answer

potential at point (1,0) , V = kq1/r = 9*10^9*10*10^-6/1 = 90 kV part (b)

potential at point (2,0) , V = kq1/r = 9*10^9*10*10^-6/2 = 45 kV

=> workdone in moving a charge fron(1,0) to (2,0) is w = q2*dV = 20*10^-6*45*10^3 = 0.9 J part (a)

=> potential difference between (1,0) and (2,0) , dV = 45 kV part (c)

potential difference between (1,0) and (0,1) , dV = 0 kV part (d)

workdone in moving a charge fron(1,0) to (0,1) is w = q2*dV = 0 J part(e)

integral E.dl along a circle

Electric field is constant along the cirlce

=> E .integral dl =(kq1/r^2).R limits from 0 to pi*r/2

=> integral E.dl =(9*10^9*10^10^-6/1^2)*(pi*1/2) = 141.37 kJ/C part (f)

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