Question

Two rods of equal length, one with a uniform positive linear charge density of +1.5 × 10?9 C/m and the other with a uniform negative linear charge density of -1.5 × 10?9 C/m, are bent to form semicircles each of radius 0.3 m. These semicircles are then joined to make a full circle. What is the magnitude of the electric field at the center of the circle?

The answer is 180 N/C

Answer 1

Here, c = charge density = +1.5 * 10^?9 C/m and r = 0.3m.

So, electric field at the center of this semicircle is Ea = -2kc/r

where k = 9*10^9

So, Ea = -2*9*10^9*1.5 * 10^?9/0.3 = -90N/C ; which means 90N/C away from the semicircle

Similarly, for the other semicircle

c = charge density = -1.5 * 10^?9 C/m

radius r = 0.3m.

So, electric field at the center of this semicircle is E = -2*k*c / r

So, Eb = -2*9*10^9*-1.5 * 10^?9 /0.3 = 90N/C ; which means 90N/C towards the semicircle

Now,both the semicircles are making a circle. So, both the fields are towards the same semicircle, so they add up as 90+90 = 180N/C