A small sphere that carries a charge q is whirled in a circle at the end of an insulating string. The angular frequency of rotation is ω. What average current does this rotating charge represent? (Use any variable or symbol stated above as necessary.)

i = qω/2π

Explanation:

Since the charge moves in a circle, its velocity v = rω. where r is the radius of the circle and ω the angular frequency of the charge.

The distance it covers in one cycle is the circle's circumference,d = 2πr.

The time it takes to cover this distance, t = d/v = 2πr/rω = 2π/ω

We know that current i = charge/time = q/t = q/2π/ω = qω/2π

So, the average current, i = qω/2π

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day