GUIDE TO RIGHT HAND RULES
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There are four right-hand rules we have used in PH 1121. Here's an overview of the four rules and how they are used (disclaimer: modified from Brown University Physics 4 Site):
1. Vector product (vector A cross vector B) (for example F = qv X B or F = IL x B or ds x r): This rule applies anytime you see two vectors with the cross in between. Put the fingers of your right-hand along the first vector. Orient your hand so that the second vector emerges from your palm (i.e., the tail of the second vector sits in your palm; alternatively, orient your hand so you can curl your fingers from the first vector towards the second). Your extended thumb gives the direction of the product. Remember: the vector you produce must be perpendicular to the other two. Your thumb tells you which of the two perpendicular directions to choose.
Also: look at Koleci's Linear Right Hand Rule.
2. Magnetic dipole moment "mu": Use this rule when you have charge circulating around in a loop and you want to find the magnetic dipole moment (you would need this if the loop were placed in a magnetic field and you want to find the orientation of the loop, namely with its "mu" vector parallel to B). Let your fingers curl around the loop following the flow of the current. Your extended thumb gives the direction of "mu". Remember: "mu" is defined so that it is always perpendicular to the plane of the loop. The magnitude of "mu" is given by the product of the current and the area of the loop.
3. Magnetic field around a current-carrying wire: The magnetic field lines around a wire are circles centered on the wire. To find the direction of the arrow on the field line (i.e. the direction of the B vector), put your extended thumb along the direction of the current flow. Your fingers will curl around in the direction of the arrow of the field line.
4. Lenz's Law: To determine the direction of the
induced current, point your right thumb in the direction of the induced magnetic
field, and your right hand fingers will curl in the direction of the induced
current.