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. A positively charged thin metal ring of radius R is fixed in the xy plane its centre at the origin 0. Anegatively charged particle P is released from rest at the point (0, 0, z 0 ) where z 0 > 0. Then the motion of P is (a) periodic, for all values of z 0 , satisfying 0 0 (b) simple harmonic, for all values of z o satisfying 0 0 ≤ R (c) approximately simple harmonic, provided z 0 (d) such that P crosses O and continues to move along the negative z axis towards z = - ∞

. A positively charged thin metal ring of radius R is fixed in the xy plane its centre at the origin 0.Anegatively charged particle P  is released from rest at the point (0, 0, z0) where z0> 0. Then the motion of P is
 
(a) periodic, for all values of z0, satisfying 0 0
(b) simple harmonic, for all values of zo satisfying 0 0≤ R
(c) approximately simple harmonic, provided z0
(d) such that P crosses O and continues to move along the negative z axis towards z = - ∞

Grade:11

1 Answers

Kevin Nash
askIITians Faculty 332 Points
7 years ago
Hello Student,
Please find the answer to your question
. (a, c) Let Q he the charge on the ring, the negative charge – q is released from point P (0, 0,Zo). The electric field at Pdue to the charged ring will be along positive z-axis and its magnitude will be
E = 1/ 4πε0 QZ0/(R2 +Z20)3./2
Therefore, force on charge P will be towards centre as shown, and its magnitude is
Fe = qE = 1/4πε0Qq/(R2 + Z20)3/2 Z0
Thanks
Kevin Nash
askIITians Faculty

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