Problem 20.66 The electric field on the axis of a uniformly charged ring has mag

Question

Problem 20.66 The electric field on the axis of a uniformly charged ring has magnitude 350kN/C at a point 6.8cmfrom the ring center. The magnitude 21cm from the center is 150kN/C ; in both cases the field points away from the ring. Part A Find the ring's radius. Express your answer using two significant figures. R =   cm   SubmitGive Up Part B Find the ring's charge. Express your answer using two significant figures. Q =   nC   Problem 20.66 The electric field on the axis of a uniformly charged ring has magnitude 350kN/C at a point 6.8cmfrom the ring center. The magnitude 21cm from the center is 150kN/C ; in both cases the field points away from the ring. Part A Find the ring's radius. Express your answer using two significant figures. R =   cm   SubmitGive Up Part B Find the ring's charge. Express your answer using two significant figures. Q =   nC   Problem 20.66 Problem 20.66 The electric field on the axis of a uniformly charged ring has magnitude 350kN/C at a point 6.8cmfrom the ring center. The magnitude 21cm from the center is 150kN/C ; in both cases the field points away from the ring. The electric field on the axis of a uniformly charged ring has magnitude 350kN/C at a point 6.8cmfrom the ring center. The magnitude 21cm from the center is 150kN/C ; in both cases the field points away from the ring. The electric field on the axis of a uniformly charged ring has magnitude 350kN/C at a point 6.8cmfrom the ring center. The magnitude 21cm from the center is 150kN/C ; in both cases the field points away from the ring. Part A Find the ring's radius. Express your answer using two significant figures. R =   cm   SubmitGive Up Part B Find the ring's charge. Express your answer using two significant figures. Q =   nC   Part A Find the ring's radius. Express your answer using two significant figures. R =   cm   SubmitGive Up Part A Find the ring's radius. Express your answer using two significant figures. R =   cm   SubmitGive Up R =   cm   R =   cm   SubmitGive Up Part B Find the ring's charge. Express your answer using two significant figures. Q =   nC   Part B Find the ring's charge. Express your answer using two significant figures. Q =   nC   Q =   nC   Q =   nC   R =   cm  

Explanation / Answer

electric field E due to point charge q at distance x   due to Ring of Raidus

is given by E = qx/(4pi eo) *(1/(x^2+ R^2)^3/2

so here E2/E1 = x'^2 + R^2/(x^2+R^2)]^3/2

( 0.21^2 + R^2)/(0.068^2 + R^2) = 350/150 = 2.34

0.0441 +R^2 = 2.34^(2/3)   *(0.004624 +R^2)

R^2 +0.0041   = 0.0081   + 0.667 R^2

R^2(1-0.667) = 0.0081-0.0041

R^2 = 0.004/(1-0.667)

R = 11 cm

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now use   E = qx/(4pieo) *( 1/(x^2+R^2) ^3/2

qx = 350000* 4*3.14 e-7 * 8.85e-12 * (0.068^2 + 0.11^2) ^1.5

qx = 8.414e-15

charge q = 8.414e-15/0.068

q = 1.2373 *10^-13 C    or   123.73 fC

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