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Question -

Consider a uniform electricfield┬аE┬а= 3 ├Ч 103┬а├оN/C.(a) What is the flux of this field through a square of 10 cm on a side whoseplane is parallel to the┬аyz┬аplane? (b) What is the fluxthrough the same square if the normal to its plane makes a 60┬░ angle withthe┬аx-axis?



Answer -

(a)┬аElectricfield intensity,┬а┬а= 3 ├Ч 103┬а├оN/C
Magnitudeof electric field intensity,┬а= 3 ├Ч 103┬аN/C

Side of the square,┬аs┬а=10 cm = 0.1 m

Area of the square,┬аA┬а=s2┬а= 0.01 m2

The plane of the square isparallel to the┬аy-z┬аplane. Hence, angle between the unitvector normal to the plane and electric field,┬а╬╕┬а= 0┬░

Flux (╬ж) through the planeis given by the relation,

╬ж=┬а

= 3 ├Ч 103┬а├Ч 0.01├Ч cos0┬░

= 30 N m2/C

(b)┬аPlanemakes an angle of 60┬░ with the┬аx-axis. Hence,┬а╬╕┬а=60┬░

Flux,┬а╬ж┬а=

= 3 ├Ч 103┬а├Ч 0.01├Ч cos60┬░

┬а= 15 N m2/C

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