Example 1: Torque on a Loop of Wire

  • A loop of wire carrying current I is placed in a magnetic field. Determine the net torque around the axis of rotation due to the current in the wire.

    1 I Axis of Rotation

Magnetic Field due to a Current-Carrying Wire

  • Moving charges create magnetic fields

  • Current-carrying wires carry moving charges, therefore they create B fields

  • Direction given by right-hand rule

  • For multiple wires, determine B field from each and add them up using superposition

  • B fields may interact with other moving charges, so current-carrying wires can exert forces upon each other.

First Right Hand Rule

EIe«ric сштетн В Мадпсьслсм В

  • "Hold" wire with your right hand, thumb in direction of positive current flow

  • Your fingers wrap in the direction of the magnetic field

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  • C:\\266298A5\\73477446-49B2-471B-AFDD-BCD03931DCDD\_files\\image385.png

Example 2: Magnetic Field due to a Wire

  • A wire carries a current of 6 amperes to the left.

  • Find the magnetic field at point P, located 0.1 meters below the wire

    0.1 m

Force Between Parallel Current-Carrying Wires

  • Use right hand rules to determine force between parallel current-carrying wires

  • Find magnetic field due to first wire. Draw it.

  • Find direction of force on second wire due to current in second wire. Force on the first wire will be equal and opposite (Newton's third Law)

    wires attract each other

Gauss's Law for Magnetism

  • You can never draw a closed surface with any net magnetic flux because there are no magnetic monopoles.

  • This is the basis of Gauss's Law for Magnetism (Maxwell's second equation)

  • C:\\266298A5\\73477446-49B2-471B-AFDD-BCD03931DCDD\_files\\image388.png

    B•d = O E.dÂ=

Example 3: Field due to Wires

  • Two long current-carrying wires are separated by a distance d as shown.

  • What is the net magnetic field due to these wires at point P, located midway between the two wires, if the top wire carries a current of 3A and the bottom wire caries a current of 5A.

  • 4 vs

Example 4: Force on a Wire

  • A 5-m long straight wire runs at a 45-degree angle to a uniform magnetic field of 5 T. If the force on the wire is 1N, determine the current in the wire

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2009 Free Response Question 2

5.0 x 10-61112 9.0 v A 9.0 V battery is connected to a rectangular
 bar of length 0.080 m, uniform cross-sectional area 5.0 x 10 m and
 resistivity 4.5 x 10 , as shown above. Electrons are the sole charge
 carriers in the bar. The wires have negligible resistance. The switch
 in the circuit is closed at time t = O . (a) Calculate the power
 delivered to the circuit by the battery. (b) On the diagram below,
 indicate the direction of the electric field in the bar. b Side View
 Explain your answer. (c) Calculate the strength of the electric field
 in the bar. A uniform magnetic field of magnitude 0.25 T perpendicular
 to the bar is added to the region around the bar, as shown below. 5.0
 x 10-61112 x a X X 9.0 v 0.25 T (d) Calculate the magnetic force on
 the bar. X X X x x X X X x X X X X X X X x X X X x X X X X x X x X b x
 X Side View

Eş\!\!\] z 72-2 z : 3 (2 u 22 91 • S •

(e) The electrons moving through the bar are initially deflected by
 the external magnetic field. On the diagram below, indicate the
 direction of the additional electric field that is created in the bar
 by the deflected electrons. Side View (f) The electrons eventually
 experience no deflection and move through the bar at an average speed
 of 3.5>< 10 3 m/s . Calculate the strength of the additional
 electric field indicated in part (e).


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