A uniformly charged ring of radius 10.0 cm has a total charge of 75.0 mC. Find the electric field on the axis of the ring at (a) 1.00 cm, (b) 5.00 cm, (c) 30.0 cm, and (d) 100 cm from the center of the ring.

(a) 6650246.305 N/C

(b) 24150268.34 N/C

(c) 6408227.848 N/C

(d) 665024.6305 N/C

Explanation:

Given:

Radius of the ring (r) = 10.0 cm = 0.10 m           [1 cm = 0.01 m]

Total charge of the ring (Q) = 75.0 μC =    [1 μC = 10⁻⁶ C]

Electric field on the axis of the ring of radius 'r' at a distance of 'x' from the center of the ring is given as:

Plug in the given values for each point and solve.

(a)

Given:

,

Electric field is given as:

(b)

Given:

,

Electric field is given as:

(c)

Given:

,

Electric field is given as:

(d)

Given:

,

Electric field is given as:

the duration of a photographic flash is related to an rc time constant, which is 0.100 μs for a certain camera.