L28_a - MAGNETIC FIELD AROUND CURRENT-CARRYING WIRES How...

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Unformatted text preview: MAGNETIC FIELD AROUND CURRENT-CARRYING WIRES How will we tackle this? Plan: 1 st : Will look at contribution B d r to the total magnetic field at some point in space due to the current in a small segment s d r of wire • Biot-Savart Law 2 nd : Will use Biot-Savart Law to find B r along the axis of a current loop. 3 rd : Will use Biot-Savart Law to get result for field around a “long” wire • a I B π µ 2 = dir. by RH-rule, m/A T 10 4 7 ⋅ × = − π µ 4 th : Will look at force between parallel current-carrying wires 5 th : Ampere’s Law: another way to get a I B π µ 2 = for field around long wire s dB I I I B BIOT-SAVART LAW (22.7) Expression for contribution B d r to magnetic field at P due to current I in small segment s d r of wire • r ˆ is UNIT VECTOR pointing s d r → P • r is DISTANCE from s d r → P • θ is the ANGLE between s d r and r ˆ Then contribution to B r at P from s d r is 2 ˆ 4 r r s d I B d × = r r π µ • m/A T 10 4 7 ⋅ × = − π µ is the permittivity of free space • Direction of B d r is from r s d ˆ × r (can also use RH-rule with thumb → current) I ds r P θ r BIOT-SAVART LAW: understanding 2 ˆ 4 r r s d I B d × = r r π µ • For drawing, direction of r s d ˆ ×...
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L28_a - MAGNETIC FIELD AROUND CURRENT-CARRYING WIRES How...

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