Question

The figure shows two concentric rings of radii R and R 2.17R, that lie on the same plane. Point P lies on the central z axis, at distance D = 2.11R from the center of the rings. The smaller ring has uniformly distributed charge Q 3.07 x 106 C. What is the uniformly distributed charge on the larger ring if the net electric field at P is zero? Number the tolerance is +/-5% Click if you would like to Show Work for this question: Units Qpen Show Work

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Answer #1

given

R and R ' = 2.17 R

D = 2.11 R

Q = 3.07 x 10-6 C

when the net electric field is zero at point P

so E = ( k Q D / ( D2 + R2 )3/2 ) + ( k Q' D / ( D2 + (2.17R)2 )3/2 ) = 0

Q / ( D2 + R2 )3/2 ) = - Q' / ( D2 + (2.17R)2 )3/2 )

Q ' = - Q ( (2.11R)2 + (2.17R)2)3/2 / ( (2.11R)2 + R2 )3/2

= - Q ( 4.452 + 4.7089 )3/2 / ( 4.452 + 1 )3/2

= - Q x 2.178

Q ' = - 3.07 x 10-6 x 2.178

Q ' = - 6.6866 x 10-6 C

the uniformly distributed charge on the larger ring if the electric field is zero is Q ' = - 6.6866 x 10-6 C

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