help... I don\'t understand how they got the answer to these two questions... l

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help... I don't understand how they got the answer to these two questions...

l s to identify the the exam version you have identify IMPORTANT This is to identify the exam version you have the C A solid metal sphere is at the center of a hollow metal sphere, as shown. The net charge on the inner sphere is -2 uC and the electric field one meter outside of the outer shell points outwards. The net charge of the outer shell Qs must be: 1) None of these 0 3) Q's 2 A solid metal sphere is at the center of a hollow metal shell, as shown. The radius of the inner sphere is 10 cm and the inner and outer radii of the hollow shell are 20 cm and 30 cm The net charge on the inner sphere is +20 uC and the electric field just outside the outer shell [but essentially at 30 cm] is 107 NIC pointing inwards. The net charge on the outer shell is: a) one of these b) 330 LLC d) 100 LLC 0 LLC

Explanation / Answer

a) The inner surface of hollow sphere will acquire cahrge of - 2 micro columbs due to induction, The outer surface will get + ve charge due to induction, therefore it must have more than 2 micro columb for electric field to pojnt outwards, as electric field is always directed out of positive charge.

Q.4 : E = K Q/ r^2

10^7 = 9 x 10^9 ( Q) / ( 0.3)^2

Q = 0.09 x 10^7 / 9 x 10* 9 = 0,01 x 10^ -2 = 1 x 10^-4 = -100 x 10^-6 C ( as the elctric field is pointing inwards) .

The inner surface will acquire -20 micro C charge due to induction , outer surface will acquure + 20 micro , therefore

The net charge on outer surface should is - 100 = + 20 + Q

Q = -120 micro C

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