If $\mathrm{E}_{\mathrm{a}}$ and $\mathrm{E}_{\mathrm{q}}$ represent the electric field intensity due to a…

If $\mathrm{E}_{\mathrm{a}}$ and $\mathrm{E}_{\mathrm{q}}$ represent the electric field intensity due to a short dipole at a point on its axial line and on the equatorial line at the same distance ' $r$ ' from the centre of the dipole, then
  1. $\mathrm{E}_{\mathrm{a}}=\mathrm{E}_{\mathrm{q}}$
  2. $\mathrm{E}_{\mathrm{a}}=\frac{1}{2} \mathrm{E}_{\mathrm{q}}$
  3. $\mathrm{E}_{\mathrm{a}}=\frac{1}{\sqrt{2}} \mathrm{E}_{\mathrm{q}}$
  4. $\mathrm{E}_{\mathrm{a}}=\mathrm{2E}_{\mathrm{q}}$

Solution

Given data: Dipole Concept used: Electric dipole Expression for electric field strength at a point on the axial line is $E_a=\frac{1}{4 \pi \epsilon_0} \frac{2 \overrightarrow{\mathrm{p}}}{r^3}$ Expression for electric field strength at a point on the equatorial line is $E_q=\frac{1}{4 \pi e_0} \frac{\overrightarrow{\mathrm{p}}}{r^3}$ From theabove two equations $E_a=2 E_q$

Asked in: MHT CET 2023 (14 May Shift 2)

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