A solid non conducting sphere have Two spherical cavities a and b of radius ra and rb

Text Solution

`(1)/( 4 pi epsilon_(0)) (q_(a))/(r^(2))``(1)/( 4 pi epsilon_(0)) (q_(a))/(r^(2))``(1)/( 4 pi epsilon_(0)) ( q_(a) + q_(b))/( r^(2))`zero

Answer : A

Solution : i. `sigma_(A) = ( - q_(a))/(4 pi a^(2)) , sigma_(B) = (-q_(b))/( 4 pi b^(2)) ,sigma_(R) = ( q_(a) + q_(b))/( 4 pi R^(2))` <br> ii. `E = (1)/( 4 pi epsilon_(0)) ( q_(a) + q_(b))/(r^(2))` ( Fig. S2.56)` <br> iii. `E_(a) = (1)/( 4 pi epsilon_(0)) (q_(a))/( r^(2))` <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/BMS_V03_C02_E01_115_S01.png" width="80%">

A non conducting sphere of radius R has a spherical cavity of radius R/2 as shown .the solid part of sphere has a uniform vol. Charge density p. Find magnitude and direction of electric field at a pt a) O b) A ( O IS AT CENTRE, A IS AT SURFACE OF SPHERE OF RADIUS R)

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