P23_019

P23_019 - 19. The electric ﬁeld at a point on the axis of...

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Unformatted text preview: 19. The electric ﬁeld at a point on the axis of a uniformly charged ring, a distance z from the ring center, is given by qz E= 4πε0 (z 2 + R2 )3/2 where q is the charge on the ring and R is the radius of the ring (see Eq. 23–16). For q positive, the ﬁeld points upward at points above the ring and downward at points below the ring. We take the positive direction to be upward. Then, the force acting on an electron on the axis is F =− For small amplitude oscillations z eqz . 4πε0 (z 2 + R2 )3/2 R and z can be neglected in the denominator. Thus, F =− eqz . 4πε0 R3 The force is a restoring force: it pulls the electron toward the equilibrium point z = 0. Furthermore, the magnitude of the force is proportional to z , just as if the electron were attached to a spring with spring constant k = eq/4πε0 R3 . The electron moves in simple harmonic motion with an angular frequency given by k eq ω= = m 4πε0 mR3 where m is the mass of the electron. ...
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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