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Please please IITians help me in this question. A sphere of radius R is centred at origin and is placed in uniform electrostatic field of intensity E 0 /√2 i ^ +E 0 /√2j ^ .A quater of the sphere ,lying in the 3rd quadrant is cut out.Find the flux through the remaining curved surface of sphere Ans-E 0 πR 2 /√2

Please please IITians help me in this question. A sphere of radius R is centred at origin and is placed in uniform electrostatic field of intensity E0/√2 i^+E0/√2j^.A quater of the sphere ,lying in the 3rd quadrant is cut out.Find the flux through the remaining curved surface of sphere
Ans-E0πR2/√2

Grade:12th pass

2 Answers

Arun
25750 Points
3 years ago
ϕplain​+ϕcurve​=0 or ϕplain​=−ϕcurve​
A1​=−2πR2​i^,A2​=−2πR2​j^​
E=Ecos45∘i^+Esin45∘j^​
2​E​i^+2​E​j^​
ϕ=E⋅(A1​+A2​)
2​−E​2πR2​−2​E​2πR2​=2​−πR2E​
Thus is the flux entering. So flux is 2​πR2E​
Vikas TU
14149 Points
3 years ago
ϕpla∈+ϕcurve=0
or
ϕpla∈=−ϕcurve
A→1=−πR^2/2iˆ,
A→2=−πR^2/2jˆ
E→=Ecos45∘iˆ+Esin45∘jˆ
=E/√2iˆ+E/√2jˆ
ϕ=E→⋅(A→1+A→2)
=−E/√2πR2^/2−E/√2 πR^2/2=−πR^2E/√2
This is the flux entering. So flux is πR^2E/√2.

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