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JEE MAIN Physics QUESTION #986
Question 1
For a short dipole placed at origin \(O\), the dipole moment \(P\) is along the \(x\)-axis. If the electric potential and electric field at \(A\) (on the \(x\)-axis at distance \(r\)) are \(V_0\) and \(E_0\) respectively, then the electric potential and electric field at point \(B\) on the \(y\)-axis at distance \(2r\) are:
  • \(V_0\) and \(\dfrac{E_0}{4}\)
  • zero and \(\dfrac{E_0}{16}\)✔️
  • zero and \(\dfrac{E_0}{8}\)
  • \(\dfrac{V_0}{2}\) and \(\dfrac{E_0}{16}\)
Correct Answer Explanation
On the equatorial axis (y-axis): \(V=0\) always. \(E_{axial}=\frac{2kP}{r^3}\) and \(E_{equatorial}=\frac{kP}{r^3}\). At distance \(r\): \(E_0=\frac{2kP}{r^3}\). At distance \(2r\) on equatorial: \(E=\frac{kP}{(2r)^3}=\frac{kP}{8r^3}=\frac{E_0}{16}\). So: zero and \(\frac{E_0}{16}\).