<p>A uniform circular ring of charge Q=4.10microCoulombs and radius R=1.30 cm is
ID: 2049351 • Letter: #
Question
<p>A uniform circular ring of charge Q=4.10microCoulombs and radius R=1.30 cm is located in the x-y plane, centered on the origin as shown in the figure.<br /><br /><img 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" alt="" /></p><p>What is the magnitude of the electric field, E at point P located at z=2.90 cm ?</p>
<p>Consider other locations along the positive z-axis. At what value of z does <em>E </em> have its maximum value?</p>
Explanation / Answer
Given
charge on the ring q = 4.10 C
radius of the ring r = 1.30 cm = 0.013m
distance between point and the ring z = 2.9 cm =0.029 m
magnitude of electric field at point p
E = ( 1 /4o ) ( Q z / (r2+z2 )3/2 )
= (9*109 ) ( 4.1*10-6 )( 0.029) /(0.0132 +0.0292 ) 3/2
= 3.33*107 N/C
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