S13Phys2BaLec29A

# Via rhr current to the right magnetic field out of

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Via RHR: Current to the right. Magnetic field out of the board. Force is down toward wire 2. The magnitude of the force will be: F = I 1 B 2 sin θ = I 1 μ o I 2 2 π a

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Force Between 2 Wires In general, the force per unit length for two wires separated by a distance d is: The directions can be reduced to: Parallel conductors carrying currents in the same direction attract each other. Parallel conductors carrying currents in the opposite directions repel each other.
Biot-Savart Law The proper (and ugliest way) to handle the current from a current carrying wire is the Biot-Savart Law, which states that for a differential current the magnetic field is given by: But most of the time you can find the direction with RHR and then you merely have to focus on the magnitude of the Biot- Savart Law: d ! B = μ o 4 ! Id ! s ! ˆ r r 2 dB = μ o 4 ! Ids sin " r 2

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For a complete circle ( ϕ = 2 π ): Biot-Savart Law For example, let’s find the magnetic field at the center C of a curved section of wire of radius R that covers an angle ϕ and carries a current i: Note that ds and r are always perpendicular: Use ds = Rd ϕ to integrate over the arc to find: dB = μ o 4 ! i ds sin90 ° R 2 = μ o 4 ! i ds R 2 B = dB ! = μ o 4 ! i Rd " R 2 0 " ! B = μ o 4 ! i R d " 0 " ! B center of circular arc = μ o i ! 4 " R B center = μ o i 2 R
For Next Time (FNT) Keep reading Chapter 29 Finish working on the homework for Chapter 28
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