Question

A large number of positive charges, each of magnitude $ q $, are placed along the x-axis at the origin and at every 1 cm distance in both directions. The electric flux through a spherical surface of radius 2.5 cm centered at the origin is:

• A. \( \dfrac{5q}{\varepsilon_0} \)
• B. \( \dfrac{8q}{\varepsilon_0} \)
• C. 0
• D. \( \infty \)

Hint:

Electric flux through a closed surface depends only on net charge enclosed: \( \phi = \frac{q_{\text{enclosed}}}{\varepsilon_0} \)

Answer 1

The Correct Option is A

Given that charges are placed at every 1 cm interval along the x-axis, and the sphere has radius 2.5 cm:
Number of charges enclosed = from \( -2\, \text{cm} \) to \( +2\, \text{cm} \) (excluding boundary at \( \pm2.5\, \text{cm} \))
Positions: \( -2\,\text{cm}, -1\,\text{cm}, 0, +1\,\text{cm}, +2\,\text{cm} \) → Total 5 charges.
Using Gauss’s Law: \[ \phi = \frac{q_{\text{enclosed}}}{\varepsilon_0} = \frac{5q}{\varepsilon_0} \]