Question

A point charge causes an electric flux of \(−1.0 × 10^3 Nm^2 C^{-1}\) to pass through a spherical Gaussian surface of 10.0 cm radius centered on the charge. 
(a) If the radius of the Gaussian surface were doubled, how much flux would pass through the surface? 
(b) What is the value of the point charge?

Answer 1

(a) Electric flux, \(Φ = −1.0 × 10^3 N m^2C^{-1}\)
Radius of the Gaussian surface, \(r = 10.0\,cm\)
Electric flux piercing out through a surface depends on the net charge enclosed inside a body. It does not depend on the size of the body. If the radius of the Gaussian surface is doubled, then the flux passing through the surface remains the same i.e., \(−10^3 N m^2C^{-1}.\)

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(b) Electric flux is given by the relation
                                       \(\phi= \frac{ q}{ε_0}\)
Where,
\(ε_0\)= Permittivity of free space \(= 8.854 × 10^{−12} N^{−1}C^2 m^{−2}\)
\(q\)= Net charge enclosed by the spherical surface =\(\phi ε_0\)
\(= −1.0 × 10^3 × 8.854 × 10^{−12}\)
= \(−8.854 × 10^{−9} C\)
= \(−8.854 nC\)
Therefore, the value of the point charge is \(−8.854 nC\).