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Sunday, April 13, 2014

How to do Biot-Savart (B-S) for Moving Point Charges

Perhaps the most challenging part of magnetism for students is Biot-Savart rule.  This is the general rule that is used to find the strength and direction of magnetic fields created by moving charged particles or currents. In this video, the focus is on how to do B-S for point charges.

The B-S rule has a cross product in it, which is necessary due to the nature of Nature - Nature chose to have magnetic fields from moving charges circulate around that moving charge!  How do we handle circulating vectors?!?!?!  Well, you guessed it, with cross products.

The strength of the B-field from a moving charge ends up being B = (10^-7)qvsin(theta) / r^2.  In this expression, theta is the angle between the motion of the particle (velocity) and the radial line from the charge to the point you are finding the B-field.  What this means, by the way, is that magnetism is strongest at points perpendicular to the line of motion, and B = 0 if you are behind or in front of the moving charge, since sin(180) = 0 and sin(0) = 0, respectively.

Check out the examples, and hopefully this will help a bit.

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