   Chapter 20, Problem 11P

Chapter
Section
Textbook Problem

Inductive charging is used to wirelessly charge electronic devices ranging front toothbrushes to cell phones. Suppose the base unit of an inductive charger produces a 1.00 × 10−3-T magnetic Held. Varying this magnetic Held magnitude changes the flux through a 15.0-turn circular loop in the device, creating an emf that charges its battery. Suppose the loop area is 3.00 × 10−4 m2 and the induced emf has an average magnitude of 5.00 V. Calculate the time required for the magnetic field to decrease to zero from its maximum value.

To determine
Time required for the magnetic field to decrease to zero from its maximum value.

Explanation

Given Info: magnetic field is 1×103T , number of turn is 15turns , area of the coil is 3×104m2 and emf in the coil  is 5V.

Formula for induced emf,

ε=NΔϕBΔt

• ΔϕB is the change in magnetic flux
• Δt is the change in time
• N is the number of turns

Formula to calculate the magnetic flux is,

ϕBΔt=A(ΔBΔt)

• B is the magnetic field,
• ΔA is the change in area of the loop

The magnetic field decreases from maximum to zero, now the magnetic flux becomes,

ϕB=BA

Rearrange the expression in terms of Δt

x

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