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PHY110W MAGNETISM <strong>MAGNETIC</strong> <strong>FIELDS</strong> <strong>DUE</strong> <strong>TO</strong> <strong>CURRENTS</strong><br />
<strong>MAGNETIC</strong> FIELD <strong>DUE</strong> <strong>TO</strong><br />
A MOVING CHARGE<br />
From the Biot-Savart law, the field due to a differential<br />
current element ids is given by<br />
<br />
µ 0 ids×<br />
r<br />
dB =<br />
4π<br />
3<br />
r<br />
<br />
Setting ds =<br />
<br />
dQ<br />
v dt , and i = , we get<br />
dt<br />
<br />
µ 0 dQ v × r<br />
dB =<br />
4π<br />
3<br />
r<br />
If we define the differential charge element dQ as the<br />
charge on a single particle contributing to the current,<br />
then the magnetic field due to a moving charged<br />
particle is given by<br />
<br />
µ 0 qv × r<br />
B =<br />
4π<br />
3<br />
r<br />
As before, the direction of B is given by the direction<br />
<br />
of the cross product v × r , or the right hand curled<br />
fingers rule.<br />
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