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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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BuyFindarrow_forward

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

A technician wearing a circular metal band on his wrist moves his hand into a uniform magnetic field of magnitude 2.5 T in a lime of 0.18 s. If the diameter of the band is 6.5 cm and the field is at an angle of 45° with the plane of the metal hand while the hand is in the field, find the magnitude of the average emf induced in the band.

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To determine
Magnitude of average induced emf in the band

Explanation

Given Info: change in magnetic field is 2.5 T, radius of the loop is 6.5×102m , orientation of the magnetic field θ=45° , and change in time is 0.18 s.

Formula for induced emf within the circle,

ε=ΔϕBΔt

  • ΔϕB is the change in magnetic flux
  • Δt is the change in time

Formula to calculate the magnetic flux is,

ϕBΔt=A(ΔBΔt)

  • ΔB is the magnetic field,
  • A is the change in area of the loop

Simplify the above expression,

ε=ΔBAcosθΔt=A(B2B1)Δtcosθ=π

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