Question

A uniformly charged ring of radius 10.0 cm has a total charge of 74.0 μC. Find the electric field on the axis of the ring at the following distances from the center of the ring. (Choose the x-axis to point along the axis of the ring.)

a)1.00cm

b)5.00cm

c)30.00cm

d)100.00cm

Answer 1

Given that

r = 10 cm = 0.1 m

Q = 74 uC

(a)

Electric field on the axis of a ring at any distance from the center of the ring,

E = k*Q*x / (x^2 + r^2)^3/2

at x = 1 cm = 0.01 m

E = 9*10⁹*74*10^-6*0.01 / [(0.01)² + (0.1)²]^3/2

E = 6.56 * 10⁶ N/C

(b)

at x = 5 cm = 0.05 m

E = 9*10⁹*74*10^-6*0.05 / [(0.05)² + (0.1)²]^3/2

E = 23.82 * 10⁶ N/C

(c)

at x = 30 cm = 0.3 m

E = 9*10⁹*74*10^-6*0.3 / [(0.3)² + (0.1)²]^3/2

E = 6.32 * 10⁶ N/C

(d)

at x = 100 cm = 1 m

E = 9*10⁹*74*10^-6*1 / [(1)² + (0.1)²]^3/2

E = 0.656 * 10⁶ N/C