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 2EB =E1+E2 = ρR3ε0+−ρ3ε0R233R22=17ρR54ε0Ratio = EA EB =1834
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