Find the force experienced by the s...
Question
Find the force experienced by the semicircular rod charged with a charge q, placed as shown in figure. Radius of the wire is R and the infinitely long line of charge
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Find the force experienced by the semicircular rod charged with a charge q, placed as shown in figure. Radius of the wire is ( mathrm{R} ) and the infinitely long line of charge with linear density ( lambda ) is passing through its to the plane of wirn centre and perpendicular to the plane of wire.
(A) ( frac{lambda q}{2 pi^{2} varepsilon_{0} R} )
(B) ( frac{lambda q}{pi^{2} varepsilon_{0} R} )
(C) ( frac{lambda q}{4 pi^{2} varepsilon_{0} R} )
(D) ( frac{lambda q}{4 pi varepsilon_{0} R} )

JEE/Engineering Exams
Physics
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Find the force experienced by the semicircular rod charged with a charge q, placed as shown in figure. Radius of the wire is R and the infinitely long line of charge with linear density λ is passing through its to the plane of wirn centre and perpendicular to the plane of wire
Fullscreen

( d F=E cos theta d q( ) where Eistheelectricfield
ofthechargedrod Electricfieldatthelocationofthechargedq
( i s )
( E=frac{lambda}{2 pi in R} )
( d q=frac{q}{pi R} times R d theta )
( d F=frac{lambda cos theta}{2 pi in R} frac{q}{pi R} times R d theta )
( int d F=int frac{lambda cos theta}{2 pi epsilon R} frac{q}{pi} times d theta )
( F=int_{-frac{pi}{2}}^{+frac{pi}{2}} frac{lambda cos theta}{2 pi in R} frac{q}{pi} times d theta )
( F=int_{-frac{pi}{2}}^{+frac{pi}{2}} frac{lambda cos theta}{2 pi in R} frac{q}{pi} times d theta )
( F=frac{lambda q}{2 pi^{2} in R}(sin theta)^{frac{pi}{2}}=frac{2 lambda q}{2 pi^{2} in R} )
( F=frac{lambda q}{pi^{2} in R} )

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