Magnetic Fields 10 20 14 9 18 AM Magnetic forces are only present when charge is moving Amperes Experiment 1820 o o Wires will bend toward each other they will attract if the currents in the wires are the same direction parallel Wires will bend away from each other they will repel if the currents in the wires are anti parallel Force depends on o 1 amount of moving charge o 2 speed of moving charge if drift velocity is faster then the wires will bend more o 3 direction of moving charge Similar to Electric field due to a point charge o Currents lead to forces which are magnetic forces by analogy o o The right hand rule is that when you curl fingers inwards from first vector r to second vector dl then thumb is in the direction of the cross product perpendicular to both vectors B is magnetic field SI units of magnetic field are Teslas T Commonly used units are Gauss G Earth s magnetic field is about 0 5 Gauss in Tucson Arizona but it depends on time and location Strong permanent magnets o One tenth of a Tesla 0 1 T Rare Earth metals are very strong magnets Ultra High electromagnets current flowing electrons spinning magnetic moment associated with an electron in an atom the electron is moving and that causes current a few Tesla Heat power I 2 R current squared times resistance large current means large magnetic field a superconductors resistance tends to zero Highest microscopic magnetic fields 10 4 Tesla only exists in a microscopic area for a few picoseconds 10 6 Tesla stars Direction of B magnetic field is dl x r 0 is a universal constant called permeability analogous to permittivity epsilon0 0 1 26 10 6 Tesla meters Amps 0 4Pi 10 7 Magnetic field for a straight line of current Note in equation above denominator is 2 Pi x o Approximations If x L the fixed point is very close to the wire then Direction of magnetic field follows right hand rule curl fingers in the direction of current then thumb is direction of magnetic field NOTE In above approximation there is a multiplier of current on the top of the denominator Ring of current Ampere s Law Right hand rule for magnetic field direction curl fingers in direction of current and magnetic field flows in direction of thumb Reminder for electric fields o o Rules for amperes law L must be a closed loop Only current enclosed by the loop counts in Current can be positive or negative depending on Ampere s law flow If current flows along thumb when magnetic field goes along curling fingers it is positive right hand rule Infinite current wire o compare to finite wire case above Infinite Cylinder of radius a carrying uniform current I Solenoid Winding of wire around a cord spool coiling cylindrical tube wound by a wire in the form of a large number of circular loops Find B everywhere for infinitely long solenoid of radius a and current I through each turn Loop 2
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