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Question -

A point charge causes anelectric flux of −1.0 × 103 Nm2/C to pass through a spherical Gaussiansurface of 10.0 cm radius centered on the charge. (a) If the radius of theGaussian surface were doubled, how much flux would pass through the surface?(b) What is the value of the point charge?



Answer -

(a) Electric flux, Φ = −1.0 × 103 Nm2/C

Radius of the Gaussiansurface,

r = 10.0 cm

Electric flux piercing outthrough a surface depends on the net charge enclosed inside a body. It does notdepend on the size of the body. If the radius of the Gaussian surface isdoubled, then the flux passing through the surface remains the same i.e., −103 N m2/C.

(b) Electric flux is given bythe relation,

Where,

q = Net charge enclosed by the spherical surface

0 = Permittivity offree space = 8.854 × 10−12 N−1Cm−2

= −1.0 × 103 × 8.854 × 10−12

= −8.854 × 10−9 C

= −8.854 nC

Therefore, the value ofthe point charge is −8.854 nC.

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