3) A ring of radius 15 cm is injected with an amount of charge of 3.5 * 10-12C, uniformly distributed along the ring. The ring rotates with an angular velocity of 17 rad/s. Find the power radiated by the system.

Given Information:

Radius = r = 15 cm = 0.15 m

Charge = q = 3.5x10⁻¹² C

Angular velocity = ω = 17 rad/s

Required Information:

Power radiated = P = ?

Answer:

Power radiated = 1.987x10⁻¹² W

Explanation:

We know that power is given by

P = VI

Where V is the potential due to charge and is given by

V = kq/r

Where k is the coulomb constant 8.98x10⁹ N. m²/C²

V = (8.98x10⁹*3.5x10⁻¹²) / 0.15

V = 0.2095 V

we know that the rate of charge flow is current

I = q/t

where t is found by the relation

ω = 2π/t

t = 2π/ω

t = 2π/17

t = 0.369 s

so current is

I = q/t = 3.5x10⁻¹²/0.369

I = 9.485x10⁻¹² A

Therefore, the amount of power radiated is

P = VI

P = 0.2095*9.485x10⁻¹²

P = 1.987x10⁻¹² W