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Twopointchargesareplacedon they - axisaty=+aandy=- ainvacuum. Themagnitude of eachchargeisq.Determin theelectric fieldintensityatP( x ,0)on thex - axis. |
Answer» Solution :Supposeelectricfieldintensityatthe pointPdue tothe chargesatA andBare` E_ 1and E _ 2` , RESPECTIVELY `thereforeE _ 1=( 1 ) /( 4 pi in_ 0)*( q ) /(AP ^ 2 ), ` along` vec( P C ) ` `=(1 ) /(4piin _0 )*( q ) /( a ^ 2+x ^2 ),`along`vec( PC ) ` `E _ 2=( 1 ) /(4piin _0)* ( q ) /( BP^ 2 )`, along`vec( PD ) ` `=( 1 ) /( 4piin_0 )*( q ) /( a^ 2+x ^ 2) `,along`vec( PD)` `therefore E _ 1=E_ 2`(INMAGNITUDE)= E( say) Both`E _ 1and E _ 2 `areresolvedinto twoperpendicular components. It isseen that the sinecomponentsareaddedup as theyactin thesamedirection. `therefore`Field strengtatP `= 2E COSTHETA = 2xx( 1 ) /( 4piin _0 )*(q )/(( a ^ 2+ x ^ 2 )) *( x ) /( sqrt ( a ^ 2+x ^ 2 )) ` `= ( 1 ) /(4piin _0 )*( 2q x ) /(( a ^ 2 + x ^ 2)^ ( 3//2 ) ) ` |
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