Miscellaneous Notes for Ph 113. M. J. Moloney

Review material

• Cross product. C = A x B.
• A and B are two vectors defining a plane.
• C is perpendicular to A and also to B.
• Thus, C is perpendicular to the plane containing A and B.
• We find the direction of C by placing the fingers of our right hand along the direction of A and then move to naturally close the fingers, moving from the direction of A to the direction of B. The motion of the fingers is in the AB plane and the thumb is in the direction of C.
• For unit vectors i, j, k, there is a mnemonic you might find useful. Place the letters i, j, and k clockwise in a circle, so i is at the 12 o'ckock position, j is at the 4 o'clock position and k is at the 8 o'clock position. For crossing i into j, we move clockwise and arrive at +k. This tells us that ixj = k. If we were going from j to i we would be going counterclockwise, and the result would be j x i = -k. From this you should be able to see that j x k = i, and so on.

• Electric potential V is defined as work/charge or potential energy/charge. Units of V are volts, or J/C. Thus a charge +q at a potential Vi has a potential energy Ui = +qVi. If this charge moved from rest to a lower potential Vf<Vi, its potential energy would be Uf = +qVf. We could see how much kinetic energy it picked up by writing down conservation of energy: Ki + Ui = Kf + Uf. If the charge started from rest, we would have 1/2 m vf^2 = Ui-Uf = q(Vi-Vf).