Question

A uniformly charged ring of radius 10.0 cm has a total charge of 91.0

Answer 1

Radius of the uniformly charged ring is, R = 10 cm = 0.1 m

Total charge on the ring is, Q = 91 * 10^-6 C

Electric field on the axis of the ring at a distance x from the center of the ring is given by,

E = k Q / (R² + x²)^3/2

where k = 8.99 * 10⁹ N.m² / C² is the Coulomb's force constant.

We use this formula to calculate field at given points on the axis of the ring.

(a) 1.00 cm = 0.01 m

E = k Q / (R² + x²)^3/2

E = 8.99 * 10⁹ * 91 * 10^-6 / [(0.1)² + (0.01)²]^3/2

E = 818.09 * 10³ / 0.001015037

E = 805.97 MN/C $\hat{i}$

(b) 5.00 cm = 0.05 m

E = k Q / (R² + x²)^3/2

E = 8.99 * 10⁹ * 91 * 10^-6 / [(0.1)² + (0.05)²]^3/2

E = 818.09 * 10³ / 0.001397542

E = 585.38 MN/C $\hat{i}$

(c) 30.00 cm = 0.3 m

E = k Q / (R² + x²)^3/2

E = 8.99 * 10⁹ * 91 * 10^-6 / [(0.1)² + (0.3)²]^3/2

E = 818.09 * 10³ / 0.031622777

E = 25.87 MN/C $\hat{i}$

(d) 100.00 cm = 1 m

E = k Q / (R² + x²)^3/2

E = 8.99 * 10⁹ * 91 * 10^-6 / [(0.1)² + (1)²]^3/2

E = 818.09 * 10³ / 1.015037438

E = 0.805 MN/C $\hat{i}$