Question:
Two point charges \( 8 \, \mu C \) and \( -2 \, \mu C \) are located at \( x = 2 \, \text{cm} \) and \( x = 4 \, \text{cm} \), respectively on the x-axis. The ratio of electric flux due to these charges through two spheres of radii 3 cm and 5 cm with their centers at the origin is _______.
Two point charges \( 8 \, \mu C \) and \( -2 \, \mu C \) are located at \( x = 2 \, \text{cm} \) and \( x = 4 \, \text{cm} \), respectively on the x-axis. The ratio of electric flux due to these charges through two spheres of radii 3 cm and 5 cm with their centers at the origin is _______.
Updated On: Apr 10, 2026
- \( 4 : 1 \)
- \( 3 : 4 \)
- \( 4 : 3 \)
- \( 4 : 5 \)
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The Correct Option is C
Solution and Explanation
Step 1: Understanding Electric Flux.
The electric flux \( \Phi \) through a sphere due to a point charge is given by: \[ \Phi = \frac{Q}{\epsilon_0} \] where \( Q \) is the charge and \( \epsilon_0 \) is the permittivity of free space.
Step 2: Electric Flux from Charges.
The flux depends on the charge enclosed within the sphere. Since the spheres are centered at the origin, the flux depends on how much of the charge is enclosed by each sphere. The ratio of the electric flux through the spheres is determined by the distances of the charges from the origin and their contribution.
Step 3: Ratio of Fluxes.
Given that the charges are located at distances 2 cm and 4 cm, and the radii of the spheres are 3 cm and 5 cm, we calculate the ratio of electric flux through each sphere. The correct ratio of the fluxes is \( 4 : 3 \).
Final Answer: \( 4 : 3 \)
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