CBSE Class 12-science Answered
To find the electric field by dipole at the center of dipole if we make use of formula for electrical field at axial point and taking r= 0 then it comes out to be zero But if we take formula for equatorial point it does not come out to be zero I want to ask that why we can't use formula for axial point taking r=0
Asked by ajaysankhala051 | 10 Jul, 2019, 07:01: PM
Expert Answer
Let us have a dipole of dipole moment 2qr and O be its centre at axial line.
Let P be a point on equtorial line passing through centre of dipole at a distance d from centre of dipole.
If a test charge qt is placed at P , two forces F that are equal in magnitude acting on test charge
due to charges at A and B are shown in figure.
Magnitude of each force, |F| = qqt /[ (4πε) (d2 + r2 ) ] ......................(1)
if we resolve the forces into horizontal and vertical components, vertical components cancel each other
giving net resultant force 2Fcosθ
net resultant force = 2Fcosθ = 2F×d/(d2 + r2 )1/2 ...........(2)
Hence electric field EP at P is given by, EP = 2qd /[ (4πε) (d2 + r2 )3/2 ] ........................(3)
This formula given by eqn.(3) is used to get field at any point P on the equtorial line
passing through the centre O by substituting the relevant value d.
if we want to get electric field at O using eqn.(3), we can see that net resultant force 2Fcosθ = 2F, because θ = 0.
(two forces are getting merged and acting on same line )
Again the magnitude of F as given by eqn.(1) changes , because we have d= 0 .
Modified magnitude of forces on teat charge due to each charge of dipole is given by, |F| = qqt /[ (4πε) r2 ]
Hence we get net Force FO =2F and electric field at O is given by, EO = 2F/qt = 2q /[ (4πε) r2 ]
Answered by Thiyagarajan K | 11 Jul, 2019, 12:13: PM
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