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Q.

Consider  a sphere of radius R which carries a uniform charge density  ρ.  If  a sphere of radius R2  is  carved out of  it, as shown , the ratio E→AE→Bof magnitude of electric field E→Aand  E→B . respectively, at points A and B due to the  remaining portion is:

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a

1834

b

1854

c

1754

d

2134

answer is A.

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Detailed Solution

Assume charge density inside cavity and outside cavity is +ρ and −ρ respectively.​Ein=ρr3∈0        rRPoint A is inside both spheres, ​EA =E1+E2 =  ρ3ε00+−ρ3ε0R2 = −ρR6ε0Point B inside for 1 and outside for 2​EB =E1+E2 =  ρR3ε0+−ρ3ε0R233R22=17ρR54ε0Ratio = EA EB =1834
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