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प्रश्न
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.
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उत्तर
Torque, \[\tau = \text { PE sin }\theta = \left( Ql \right)\text { E sin }\theta\] ........ (1)
Here, l is the length of the dipole, Q is the charge and E is the electric field.
Potential energy,
\[\text { U = - P Ecos }\theta = - \left( Ql \right)\text {Ecos}\theta\]
Dividing (2) by (1):
\[\frac{\tau}{U} = \frac{\left( Ql \right)E\sin\theta}{- \left( Ql \right)E\cos\theta} = - \tan\theta\]
\[ \Rightarrow U = - \frac{\tau}{\tan\theta}\]
\[ \Rightarrow U = - \frac{\tau}{\tan {60}^o}\]
\[ \Rightarrow U = - \frac{8\sqrt{3}}{\sqrt{3}}\]
\[ \Rightarrow U = - 8 J\]
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संबंधित प्रश्न
- Define torque acting on a dipole of dipole moment \[\vec{p}\] placed in a uniform electric field \[\vec{E}\] Express it in the vector from and point out the direction along which it acts. Express it in the vector from and point out the direction along which it acts.
- What happens if the field is non-uniform?
- What would happen if the external field
\[\vec{E}\] is increasing (i) parallel to \[\vec{p}\] and (ii) anti-parallel to \[\vec{p}\]?
An electric dipole is placed at an angle of 30° with an electric field intensity of 2 × 105 N/C. It experiences a torque equal to 4 Nm. The charge on the dipole, if the dipole length is 2 cm, is ______.
Two charges –q each are fixed separated by distance 2d. A third charge q of mass m placed at the mid-point is displaced slightly by x(x << d) perpendicular to the line joining the two fixed charged as shown in figure. Show that q will perform simple harmonic oscillation of time period.
`T = [(8pi^3 ε_0 md^3)/q^2]^(1/2)`
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.
The midpoint of the line joining the negative and positive charges in an electric dipole is called the:
The direction of the electric field on the equatorial line of a dipole is:
For a short dipole, the ratio of the electric field on the axial line to that on the equatorial line (at the same distance r) is:
The potential energy of a dipole in an external electric field is given by:
The electric potential at a point P due to a dipole (at distance r from the centre, at angle θ from the dipole axis) is given by:
