Grade 12Electrostatics
electrostatics
a point charge q is located on axis of disc of radius r at distance b from the plane of disc.if one-fourth of electric flux from charge passes through disc then.......
(a)r = b (b)r = 2b
4 Answers
Dear Dinesh
Draw a sphere whose center is at a distance b from the disk and which cover the disk
we know that flux throug a segment which makes an angel θ at the center is
Φ=Q/2ε (1-cosθ)
where cosθ = b/(b2+r2)1/2
given flux passes in 1/4 th
so Q/2ε (1-cosθ) =Q/4ε
1-cosθ = 1/2
cosθ =1/2
b/(b2+r2)1/2 =1/2
r =√3 b
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Badiuddin
(it is disk not the spherical cap how can you take a sphere)
A 1000w laser beam is concentrated by a Lens of a cross-sectional area of 10^-5 cm^2 . find the corresponding amplitude of the electric field
Hello student
As we know total electric flux given by a point charge Q = Q/ε0
this flux is equally distributed in a solid angle of 4π
Now, if a disk makes an angle θ with the axis of charge, the solid angle covered by the disk
Ω = 2π(1- cosθ)
Hence electric flux through disk, ɸ = Q/4πε0 x 2π(1- cosθ) = Q/2ε0 x (1 – cosθ)
Given, this flux is ¼ of the flux given by charge Q
Hence,
Q/2ε0 x (1 – cosθ) = Q/4ε0
or, cosθ = ½
or, θ = 60o
Hence, b/R = cos60o
or, b = R/2
or, R = 2b
or, b = (b2 + r2)1/2/2
or, 4b2 = b2 + r2
or, r2 = 3b2
or, r = √3 b
Hope it helps
Regards,
Kushagra
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