   Chapter 20, Problem 12P

Chapter
Section
Textbook Problem

Medical devices implanted inside the body are often powered using transcutaneous energy transfer (TET), a type of wireless charging using a pair of closely spaced coils. An emf is generated around a coil inside the body by varying the current through a nearby coil outside the body, producing a changing magnetic flux. Calculate the average induced emf if each 10-turn coil has a radius of 1.50 cm and the current in the external coil varies from its maximum value of 10.0 A to zero in 6.25 × 10−6 s. (Hint: Recall from Topic 19 that the magnetic field at the center of the current-carrying external coil is B = N μ 0 I 2 R . Assume this magnetic field is constant and oriented perpendicular to the internal coil.)

To determine
Average Induced emf in each turn of a coil.

Explanation

Given Info: current in the coil is 10A, number of turns is 10, radius of the coil is 1.5×102m2

Formula for maximum magnetic field,

Bmax=NμoI2R

• R is the radius of the coil
• N is the number of turns in the coil
• is the current in the coil

Substitute 10 turns for N, 10A for I, 1.5×102m2 for A and 4π×107Tm/A in the above expression to get Bmax

Bmax=10turns(4π×107Tm/A)(10A)2(1.5×102m2)=4.19×103T

Formula for induced emf in the coil,

ε=NΔϕBΔt

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

Formula to calculate the  magnetic flux is,

ϕBΔt=B(ΔAΔt)

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