Evelyn wears glasses whose wire frames are shaped like to circles, each with an area of 2.0x10^-3 m^2. The horizontal component of the earths' magnetic field in Evelyn's hometown is 1.9x10^-5 T. If Evelyn turns her head back and forth, rotating it through 90degrees every 0.5s, what is the induced voltage in the wire frame of one eyepiece.

Question

Evelyn wears glasses whose wire frames are shaped like to circles, each with an area of 2.0x10^-3 m^2. The horizontal component of the earths' magnetic field in Evelyn's hometown is 1.9x10^-5 T. If Evelyn turns her head back and forth, rotating it through 90degrees every 0.5s, what is the induced voltage in the wire frame of one eyepiece.

Answer 1

Induced emf = - (Rate of change of magnetic flux)

= - (Change in magnetic flux)/(Change in Time)
= - d(Ф)/dt
= - (Final magnetic flux - Initial Magnetic Flux)/0.5
= - (B*A*cos(θ2) - B*A*cos(θ1))/0.5
= - B*A( cos(θ2) - cos(θ1) )/0.5

Your question gives you the value of B, of A, and gives you the difference between the two angles as 90 degrees. Plug in the values, and solve.

(The negative sign may be considered at the end since it only describes the direction of the induced emf)