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Chapter 29--Examples

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Chapter 29 examples l.jpg

Chapter 29--Examples

Problem l.jpg


  • Derive the equation relating the total charge Q that flows through a search coil (Conceptual Example 29.3 in Section 29.2) to the magnetic field B. The search coil has N turns, each with area A and the flux through the coil is decreased from its initial value to zero in a time Dt. The resistance of the coil is R and the total charge is Q=I Dt where I is the average current induced by the change in flux

From example 29 3 l.jpg

From Example 29.3

  • A search coil is a practical way to measure magnetic field strength. It uses a small, closely wound coil with N turns. The coil, of area A, is initially held so that its area vector A is aligned with a magnetic field with magnitude B. The coil is quickly pulled out of the field or rotated.

  • Initially the flux through the field is F=NBA. When it leaves the field or rotated, F goes to zero. As F decreases, there is a momentary induced current which is measured. The amount of current is proportional to the field strength.

Solution l.jpg


  • EMF=-DF/Dt

    • DF=F2–F1

      • Where F1 =NBA and F2 =0

      • DF=-NBA

    • EMF=NBA/Dt

  • V=iR where V=EMF

    • EMF=NBA/Dt=iR

    • i=NBA/RDt

  • Q=iDt=NBA/R

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Part B

  • In a credit card reader, the magnetic strip on the back of the card is “swiped” past a coil within the reader. Explain using the ideas of the search coil how the reader can decode information stored in the pattern of magnetization in the strip.

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  • The card reader contains a search coil.

  • The search coil produces high EMF and low EMF as the card is swiped.

  • A high EMF is treated as a binary 1 and a low EMF is treated as a binary 0

  • Ascii information (character codes between 1 and 64) can be stored there in a few bits (6-bits or 26).

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A circular loop of flexible iron wire has an initial circumference of 165 cm but its circumference is decreasing at a rate of 12 cm/s due to a tangential pull on the wire. The loop is in a constant, uniform magnetic field oriented perpendicular to the plane of the loop and with a magnitude of 0.5 T

  • Find the EMF induced in the loop at the instant when 9 s have passed.

  • Find the direction of the current in the loop as viewed looking in the direction of the magnetic field.

Emf df d t b d a d t l.jpg


  • F=BA

    • dF/dt=BdA/dt

    • c=2pr so A=pr2

      • r=c/2p so A=c2/4p

    • dA/dt=d/dt(c2/4p)= (2c/4p)dc/dt

    • dF/dt= B(c/2p)dc/dt

      • Where B=0.5

      • dc/dt=0.12 m/s

      • At 9s, c=1.65-.12*(9s)=0.57 m

    • dF/dt=5.44 x 10-3 V

  • Since F is decreasing, the EMF is positive. Since EMF positive, point thumb along A and look at fingers.

    • They curl counterclockwise.

Problem9 l.jpg


Suppose the loop in the figure below is

  • Rotated about the y-axis

  • Rotated about the x-axis

  • Rotated about an edge parallel to the z-axis.

    What is the maximum induced EMF in each case if A=600 cm2, w=35 rad/s, and B=.45T?

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Case a—Rotating about y-axis

Case b rotating about the x axis l.jpg

Case b—rotating about the x-axis

  • The normal to the surface is in the same direction as B during this rotation. Thus BA=constant

  • d/dt(constant)=0 so EMF=0

Case c rotating about z axis l.jpg

Case c—Rotating about z-axis

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The figure below shows two parallel loops of wire having a common axis. The smaller loop (radius r) is above the larger loop (radius R) by a distance x>>R. Consequently, the magnetic field due to current i in the larger loop is nearly constant throughout the smaller loop. Suppose that x is increasing at a constant rate, v.

  • Determine the magnetic flux though area of the smaller loop as a function of x.

  • In the smaller loop find

    • The induced EMF

    • The direction of the induced current.





Magnetic field of a circular loop l.jpg

Magnetic Field of a Circular Loop

By the RH Rule, the field is upward in the small ring

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EMF in smaller loop

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Direction of current

  • Assume that normal to smaller loop is positive upwards

  • B, then, is in positive direction

  • But F is decreasing or has a negative d dF /dt

  • A negative * negative=positive so EMF is +

  • RH Thumb in up direction, fingers curl counter clockwise!

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