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Electrostatic Potential And Capacitance

Question
CBSEENPH12037420

Charges of magnitudes 2q and – q are located at points (a, 0, 0) and (4a, 0, 0). Find the ratio of the flux of electric field due to these charges through concentric spheres of radii 2a and 8a centred at the origin.

Solution

The locations of the charges 2q(a,0,0) and -q(4a,0,0) are shown in the figure.
 
Radii of the sphere are given as 2a and 8a respectively.
Now, using the formula as per gauss law,
Electric flux through the sphere of radius 2a, ϕ1 = 1ε0(2q)
Electric flux through the sphere of radius 8a, ϕ2 = 1ε0(2q-q) 
    = 1ε0(q)

Therefore, the ratio of the flux is given as,

          ϕ1ϕ2 = 21.
      ϕ1 : ϕ2 = 2:1

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