Consider a sphere of radius 1.1m with point p at its centre. Within the sphere o

Question

Consider a sphere of radius 1.1m with point p at its centre. Within the sphere one meter out from the centre P are two charges, positioned so that if a line was drawn from each charge to P, the centre of the sphere, it would form an ange of 90 degrees. One carge is -3 micro Coulombs while the other charge is + 4 micro Coulombs.

a) What is the magnitude of the electric field(in kN/C) at P, the centre of the sphere due to the two charges? (The answer actually is 45 but I'd like to know how to arrive at that.)

b) The total electric potential at P due to the two charges(in kV). (The answer here is 9 but I'd like to know to arrive at that.)

c) A test charge of 2 x 10^-9 C is moverd from infinity to the point P. The total work done on the test charge by the electical forces due to the electric potential at P in this operation is (in microJoules)? ( Here the answer is -18 but I'd like to know how you get that)

Explanation / Answer

A)

both the charges are at a distance of 1m from the center P

then electrci filed due to point charge Q is E = k*Q/r^2

r is the distance from center to piont p

due to 4 uC is E1 = k*Q1/r1^2 = (9*10^9*4*10^-6)/1^2 = 36000 N/C = 36 kN/C

due to -3 uC is E2 = k*Q2/r2^2 = (9*10^9*3*10^-6)/1^2 = 27 kN/C

resultant electric field is E = sqrt(36^2+27^2) = 45 kN/C

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B) electric potential at P is k*(Q1-Q2)/r = (9*10^9*(4-3)*10^-6)/1 = 9kV

C) potential difference is -9kV = -9000 V

Work done is W = q*dV = -2*10^-9*9000= -18*10^-6 J = 18 micro J

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