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प्रश्न
Show that intensity of electric field at a point in broadside position of an electric dipole is given by:
E = `(1/(4 pi epsilon_0)) p/((r^2 + l^2)^(3//2))`
Where the terms have their usual meaning.
Show that intensity of electric field E at a point in broadside on position is given by:
E = `(1/(4 pi epsilon_0)) p/((r^2 + l^2)^(3//2))`,
where the terms have their usual meaning.
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उत्तर
Consider a dipole of length 2l and moment `vec p`.
From the figure, resultant electric field intensity at C:
`vec E = vec E_A + vec E_B`
`|vec E_A| = 1/(4 pi epsilon_0) q/(r^2 + l^2)`
`|vec E_B| = 1/(4 pi epsilon_0) q/(r^2 + l^2)`
Sine components of `vec E_A` and `vec E_B` get cancelled each other as `|vec E_A| = |vec E_B|`.
The cosine components get added up to give the resultant field.
i.e., E = EA cos θ + EB cos θ
= `1/(4 pi epsilon_0) * q/(r^2 + l^2) cos theta + 1/(4 pi epsilon_0) * q/(r^2 + l^2) cos theta`
= `2 * 1/(4 pi epsilon_0) * q/(r^2 + l^2) cos theta`
= `2 xx 1/(4 pi epsilon_0) * q/(r^2 + l^2) xx l/(r^2 + l^2)^(1//2)`
= `1/(4 pi epsilon_0) (q(2 l))/((r^2 + l^2)^(3//2))`
E = `1/(4 pi epsilon_0) p/((r^2 + l^2)^(3//2))` ...[as p = q(2l)]
The above expression gives the magnitude of the field. The direction of the electric field E at C is opposite to the direction of the dipole moment `vec p`.
संबंधित प्रश्न
A short electric dipole (which consists of two point charges, +q and -q) is placed at the centre 0 and inside a large cube (ABCDEFGH) of length L, as shown in Figure 1. The electric flux, emanating through the cube is:
a) `q"/"4piin_9L`
b) zero
c) `q"/"2piin_0L`
d) `q"/"3piin_0L`
An electric dipole of length 2 cm, when placed with its axis making an angle of 60° with a uniform electric field, experiences a torque of \[8\sqrt{3}\] Nm. Calculate the potential energy of the dipole, if it has a charge \[\pm\] 4 nC.
In which orientation, a dipole placed in a uniform electric field is in (i) stable, (ii) unstable equilibrium?
Answer the following question.
What is the unit of dipole moment?
When an electric dipole p is placed in a uniform electric field E then at what angle the value of torque will be maximum?
On the axis and on the equator of an electric dipole for all points ____________.
In a non-uniform electric field, electric dipole experiences:-
Polar molecules are the molecules ______.
What work must be done to rotate an electric dipole through an angle θ with the electric field, if an electric dipole of moment p is placed in a uniform electric field E with p parallel to E?
