You are shipwrecked on a deserted tropical island. you have some electrical devices that you could operate using a generator but you have no magnets. the earth's magnetic field at your location is horizontal and equal to 8.0×10−5t, and you decide to try to use this field for a generator by rotating a large circular coil of wire at a high rate. you need to produce ϵmax = 9.0v and estimate that you can rotate the coil at 30rpm by turning a crank handle. you also decide that to have an acceptable coil resistance, the maximum number of turns the coil can have is 2000.part a what area must the coil have? part b if the coil is circular, what is the maximum translational speed of a point on the coil as it rotates?

a. The cool must have an area of 17.892m^2

b. The maximum translational speed of a point on the coil as it rotates is 7.499m/s.

Explanation:

Given:

Emax = 9.0V = Ep

Maximum number of turns the coil can have (N) = 2000

Earth magnetic field (B) = 8 × 10^-5T

1. Area(m^2) = ?

Using the formula

A = Ep/NπB

= 9.0/(2000 x π x 8 × 10^-5)

= 9.0/0.503

A = 17.892m^2

b) maximum translational speed of a point on the coil as it rotates = ?

(Assuming the coil is circular)

Using the formula

v = ωr = π ×2.387m/s

= 7.499m/s.

r is determined by using A = πr^2k

double the distance = divide strength by 4

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