What current is produced by a ring with a radius of 0.5 m and a uniform positive linear charge density of 1 microCoulomb/m rotatingwith an angular frequency of 4π/s?
a. 1 microAmpere
b. 3.14 microAmpere
c. 6.28 microAmpere
d. 12.6 microAmpere
To find the current produced by a rotating ring with a given radius and linear charge density, you can use the formula for the current in a loop.
The formula for the current in a loop is given by:
I = qω/2π
where:
I = current
q = charge enclosed by the loop
ω = angular frequency
π = pi
In this case, we are given the radius of the ring (0.5 m) and the linear charge density (1 microCoulomb/m). To find the charge enclosed by the loop, we need to calculate the total charge on the ring.
To find the total charge, we can multiply the linear charge density by the length of the ring. The length of the ring is given by the formula:
L = 2πr
where:
L = length of the ring (circumference)
r = radius of the ring
Substituting the values, we have:
L = 2π(0.5) = π meters
The charge enclosed in the loop is equal to the product of the linear charge density and the length of the ring. Therefore:
q = (1e-6 C/m)(π m) = πe-6 Coulombs
We are also given the angular frequency (4π/s). Substituting the values into the formula for current:
I = (πe-6 C)(4π/s) / (2π) = 4e-6 Amps = 4 microAmps
Therefore, the current produced by the rotating ring is 4 microAmps.
Unfortunately, none of the provided answer choices match the calculated result.