Question:
The electric field intensity at a point on the axis of an electric dipole in ah is $4 \; NC^{-1}$. Then the electric field intensity at a point on the equitorial hue which is at a distance equal to twice the distance on the axial line and if the dipole is in a medium of dielectric constant $4$ is
The electric field intensity at a point on the axis of an electric dipole in ah is $4 \; NC^{-1}$. Then the electric field intensity at a point on the equitorial hue which is at a distance equal to twice the distance on the axial line and if the dipole is in a medium of dielectric constant $4$ is
Updated On: Apr 4, 2024
- $1 \; NC^{-1}$
- $\frac{1}{8} \; NC^{-1}$
- $ 16 \; \; NC^{-1}$
- $\frac{1}{16} \; NC^{-1}$
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The Correct Option is D
Solution and Explanation
As, electric field intensity on the axis,
$E_{\text {axis }}=\frac{2 k P}{r^{3}}$
$ \Rightarrow 4=\frac{2 k P}{r^{3}} $ for $ r > >a $
$ \left(\because \text { given, } E_{\text {axis }}=4\right)$
$\Rightarrow \frac{k P}{r^{3}}=2 \ldots $ (i)
Electric field intensity on equatorial line,
$E_{ eq }=\frac{k^{\prime} P}{r_{1}^{3}}$
where, $r_{1}=2 r $ and $ k'=\frac{k}{4}$
So, $E_{ eq }=\frac{k P}{4 \times 8 r^{3}} $
Now, from the E (i), we get
$E_{ eq }=\frac{2}{4 \times 8}=\frac{1}{16} NC ^{-1}$
$E_{\text {axis }}=\frac{2 k P}{r^{3}}$
$ \Rightarrow 4=\frac{2 k P}{r^{3}} $ for $ r > >a $
$ \left(\because \text { given, } E_{\text {axis }}=4\right)$
$\Rightarrow \frac{k P}{r^{3}}=2 \ldots $ (i)
Electric field intensity on equatorial line,
$E_{ eq }=\frac{k^{\prime} P}{r_{1}^{3}}$
where, $r_{1}=2 r $ and $ k'=\frac{k}{4}$
So, $E_{ eq }=\frac{k P}{4 \times 8 r^{3}} $
Now, from the E (i), we get
$E_{ eq }=\frac{2}{4 \times 8}=\frac{1}{16} NC ^{-1}$
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Concepts Used:
Electric Dipole
An electric dipole is a pair of equal and opposite point charges -q and q, separated by a distance of 2a. The direction from q to -q is said to be the direction in space.
p=q×2a
where,
p denotes the electric dipole moment, pointing from the negative charge to the positive charge.
Force Applied on Electric Dipole
