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  4. Two non-conducting spheres of radii R1 and R2 and carrying uniform volume charge densities +ρ and -ρ, respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region

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Q. Two non-conducting spheres of radii $R_1 \, and \, R_2 $ and carrying uniform volume charge densities $+\rho $ and $-\rho, $ respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping regionPhysics Question Image

JEE AdvancedJEE Advanced 2013Electric Charges and Fields

Solution:

For electrostatic field.
$E_p=E_1+E_2= \frac {\rho}{3 \varepsilon_0}C_1P+ \frac {(-\rho)}{3 \varepsilon_0}C_1P $
$ = \frac {\rho}{3 \varepsilon_0}(C_1P+PC_2) $
$ E_p= \frac {\rho}{3 \varepsilon_0}C_1C_2 $

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