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Question

Find the electric field at point O, due to the segment of a ring, whose linear charge density is 8 C/cm.
1200452_c733f7a7db7a4c9790b17716dc2a5dd2.jpg

A
9×1013V/m
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B
16×1013V/m
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C
8×1013V/m
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D
18×1013V/m
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Solution

The correct option is D 18×1013V/m

Linear charge density =8c/m
I took a small segment by, Which is θ above the xaxis with charge dq=λdy
Therefore,
d¯¯¯¯E=kλcosθdyr2
=9×109×8×cos600(4×102)2
Besides,
d¯¯¯¯E=kλrcosθdθ2
=9×109×8×cos600(4×102)
=9×4×109(102)2×12
=18×1013V/m

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