InterviewSolution
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InterviewSolution
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Obtain the equation of electric field by dipole at a point on axis of dipole. |
Answer» Solution :Let the point P be at distance R from the centre of the dipole on the SIDE of the charge q as shown in figure, then electric field by - q charge.  The electric field by `-q` charge `vecE_(-q) =-q/(4pi epsilon_(0)(r+a)^(2))hatp =(-kq)/(r+a)^(2)hatp` (`therefore` distance from `-q` to `P = r+a`).........(1) Electric field by `+q` charge. `vecE_(+q) = -q/(4pi epsilon_(0)(r-a)^(2))hatp = - (kq)/(r-a)^(2) hatp` (`therefore` distance from `+q` to P `=r -a)`.......(2) The unit field at P is `vecE =vecE_(+q) + vecE_(-q) = kq[1/(r-a)^(2) -1/(r+a)^(2)] hatp_(n)` (`therefore` From equation (1) and (2) ) `therefore vecE = kq(4ar)/(r^(2)-a^(2))^(2)hatp`..........(3) For `r gt gt a, r^(2) -a^(2) = r^(2)`, using in equation (3) `vecE= (k(4qa))/(r^(3))hatp =(2kp)/r^(3) (therefore p = q(2A))`..........(4) |
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