Electrostatics

JEE Main level, single correct, medium

267 of 311

Question 267 of 311

Two point charges 8 μC8 \, \mu C and −2 μC-2 \, \mu C are located at x=2x = 2 cm and x=4x = 4 cm, respectively on the xx-axis. The ratio of electric flux due to these charges through two spheres of radii 33 cm and 55 cm with their centers at the origin is _______.

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Answer: (C) 4:34 : 3

According to Gauss's law, the electric flux through a closed surface is given by Φ=qenclosedε0\Phi = \dfrac{q_{\text{enclosed}}}{\varepsilon_0}.

For the first sphere of radius r1=3r_1 = 3 cm centered at the origin, only the charge at x=2x = 2 cm is enclosed.

qenclosed,1=8 μCq_{\text{enclosed}, 1} = 8 \, \mu\text{C}

Φ1=8 μCε0\Phi_1 = \dfrac{8 \, \mu\text{C}}{\varepsilon_0}

For the second sphere of radius r2=5r_2 = 5 cm centered at the origin, both charges at x=2x = 2 cm and x=4x = 4 cm are enclosed.

qenclosed,2=8 μC−2 μC=6 μCq_{\text{enclosed}, 2} = 8 \, \mu\text{C} - 2 \, \mu\text{C} = 6 \, \mu\text{C}

Φ2=6 μCε0\Phi_2 = \dfrac{6 \, \mu\text{C}}{\varepsilon_0}

The ratio of the electric flux is:

Φ1Φ2=86=43\dfrac{\Phi_1}{\Phi_2} = \dfrac{8}{6} = \dfrac{4}{3}

Answer: 4:34 : 3

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