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Biot-Savart Law Biot-Savart law: μo I ds ˆr dB 4π r 2 μo I ds ˆr B 2 4π r The constant mo is called the permeability of free space mo = 4p x 10-7 T. m / A B for a Long, Straight Conductor The thin, straight wire is carrying a constant current ds ˆr dx sin θ k̂ Integrating over all the current elements μo I θ B cos θ dθ 4πa θ μo I sin θ1 sin θ2 4πa 2 1 μo I B 2πa for a Curved Wire Segment B Find the field at point O due to the wire segment I and R are constants μo I B θ 4πR q will be in radians B for a Circular Loop of Wire Consider the previous result, with a full circle q = 2p μo I μo I μo I B θ 2π 4πa 4πa 2a This is the field at the center of the loop B for a Circular Current Loop The loop has a radius of R and carries a steady current of I Find the field at point P Bx μo I a2 2 a x 2 2 3 2 Magnetic Force Between Two Parallel Conductors Two parallel wires each carry a steady current The field due to the current in wire 2 exerts a force on wire 1 of F1 = I1ℓ B2 μo I1 I 2 F1 2πa Ampere’s Law Ampere’s law states that the line integral of B ds around any closed path equals moI where I is the total steady current passing through any surface bounded by the closed path: B ds μ o I Magnetic Field of a Toroid Find the field at a point at distance r from the center of the toroid The toroid has N turns of wire B ds B( 2πr ) μ N I o μo N I B 2πr Magnetic Flux The magnetic flux associated with a magnetic field is defined in a way similar to electric flux The magnetic flux FB is FB B dA The unit of magnetic flux is T.m2 = Wb Wb is a weber Gauss’ Law in Magnetism Gauss’ law in magnetism says the magnetic flux through any closed surface is always zero: B dA 0 Earth’s Magnetic Field The Earth’s south magnetic pole is located near the north geographic pole The Earth’s north magnetic pole is located near the south geographic pole