Question

A rod 12.0 cm long is uniformly charged and has a total charge of -21.0 μC. Determine the magnitude and direction of the electric field along the axis of the rod at a point 38.0 cm from its center. 

Answer 1

Electric along the axis of a uniformly charged rod is given by:

E = k**L/(d*(L + d))

= Charge per unit length = Q/L

L = length of rod = 12 cm = 0.12 m

d = distance of point from the one end of the rod = 38 cm - L/2 = 38 cm - 12 cm/2 = 32 cm = 0.32 m

Q = total charge on rod = -21 uC = -21*10^-6 C

k = electrostatic constant = 9*10^9

E = k*(Q/L)*L/(d*(L + d)) = k*Q/(d*(L + d))

E = 9*10^9*21*10^-6/(0.32*(0.32 + 0.12))

E = 1.34*10^6 N/C

Since Charge is negative, So Electric field will be directed towards the rod.