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How to Visualize Electric Fields

The line inte...

Question

The line integral of an electric field along the circumference of a circle of radius r drawn with a point Q at the centre will be _____

\frac{1}{4 π^{2} t o} \frac{Q}{r}

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\frac{Q}{2 π ε_{0} r}

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Zero

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2 π Q r

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Solution

The correct option is C Zero
$\begin{matrix} T o c a l c u l a t e \oint \to E . \to d l \oint \to E . \to d l i s z e r o e v e r y w h e r e a l o n g t h e i n t e r g r a l w i l l b e z e r o . sin c e, \to E a n d \to d l a r e p e r p e n d i c u l a r t o e a c h o t h e r \to E . \to d l = 0 t h u s \oint \to E . \to d l = 0 H e n c e, t h e c o r r e c t o p t i o n i s C . \end{matrix}$

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The line integral of an electric field along the circumference of a circle of radius r drawn with a point Q at the centre will be _____

The correct option is C ZeroTocalculate∮→E.→dl∮→E.→dliszeroeverywherealongtheintergralwillbezero.since,→Eand→dlareperpendiculartoeachother→E.→dl=0thus∮→E.→dl=0Hence,thecorrectoptionisC.