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An electric dipole of moment P is placed in a uniform electric field E,with P parallel to E. It is then rotated by an angle theta. The work done is?
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An electric dipole of moment P is placed in a uniform electric field E...
Work done is equal to change in potential energy.
Work done= pE-pEcos(theta).
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An electric dipole of moment P is placed in a uniform electric field E...
**Electric Dipole in a Uniform Electric Field**

When an electric dipole is placed in a uniform electric field, it experiences a torque that tends to align the dipole moment with the electric field. The work done in rotating the dipole by an angle theta can be determined using the concept of torque and work.

**Torque on Electric Dipole**
- An electric dipole consists of two equal and opposite charges separated by a small distance, forming a dipole moment (P). The direction of the dipole moment is from the negative charge to the positive charge.
- When placed in a uniform electric field (E), the electric field exerts a force on the charges. The force on the positive charge is in the direction of the electric field, while the force on the negative charge is in the opposite direction.
- The forces create a torque on the dipole, which tends to rotate it. The torque (τ) acting on the dipole is given by the equation τ = P x E, where x represents the vector cross product.
- The torque causes the dipole to rotate until it aligns with the electric field or reaches a stable equilibrium position.

**Work Done**
- The work done in rotating the dipole can be calculated by considering the work done by the torque in rotating the dipole through an angle theta.
- The work done (W) is given by the equation W = τθ, where θ is the angle rotated by the dipole.
- Substituting the expression for torque (τ = P x E) into the equation, we get W = (P x E)θ.
- Since the dipole moment P and the electric field E are parallel in this case, the vector cross product P x E is equal to P * E * sin(90°) = P * E.
- Therefore, the work done can be simplified to W = P * E * θ.

**Conclusion**
In conclusion, when an electric dipole of moment P is placed in a uniform electric field E, and it is rotated by an angle theta, the work done in rotating the dipole is given by the equation W = P * E * θ. The work done is directly proportional to the dipole moment, the magnitude of the electric field, and the angle of rotation.
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The orbital and spin angular momentum of the atom influence its magnetic structure and these properties are most directly studied by placing the atom in a magnetic field. Also, a magnetic field can affect the wavelengths of the emitted photons.The angular momentum vector associated with an atomic state can take up only certain specified directions in space. This concept of space quantization was shown by Otto Stern and Walthor Gerlach in their experiment.In the experiment, silver is vapourized in an electric oven and silver atoms spray into the evacuated apparatus through a small hole in the oven wall. The atoms which are electrically neutral but have a magnetic moment, are formed into a narrow beam as they pass through a slit in a screen. The beam, thus collimated, then passes between the poles of an electromagnet and finally, deposits its silver atoms on a glass plate that serves as a detector. The pole faces of the magnet are shaped to make the magnetic field as nonuniform as possible.In a non-uniform magnetic field, there is a net force on a magnetic dipole. Its magnitude and direction depends on the orientation of the dipole. Thus the silver atoms in the beam are deflected up or down, depending on the orientation of their magnetic dipole moments with respect to the z–direction.The potential energy of a magnetic dipole in a magnetic field where is magnetic dipole moment of the atom. From symmetry, the magnetic field at the beam position has no x or y components i.e.The net force Fz on the dipole isThus, the net force depends, not on the magnitude of the field itself, but on its spatial derivative or gradient.The ResultsIf space quantization did not exist, then could take on any value from + to –, the result would be a spreading out of the beam when the magnet was turned ON. However, the beam was split cleanly into two subbeams, each subbeam corresponding to one of the two permitted orientations of the magnetic moment ofthe silver atom, as shown.In a silver atom, all the spin and orbital magnetic moments of the electrons cancel, except for those of the atoms single valance electron. For this electron the orbital magnetic moment is zero because orbital angular momentum is zero (because for electrons of s–orbit, L = 0), leaving only the spin magnetic moment. This can take up only two orientations in a magnetic field, corresponding to ms = +1/2 and ms = – 1/2. Hence there are two subbeams – and not some other number.Q.A hydrogen atom in ground state passes through a magnetic field that has a gradient of 16mT/m in the vertical direction. If vertical component magnetic moment of the atom is 9.3 × 10–24 J/T, then force on it due to the magnetic moment of the electron is

The orbital and spin angular momentum of the atom influence its magnetic structure and these properties are most directly studied by placing the atom in a magnetic field. Also, a magnetic field can affect the wavelengths of the emitted photons.The angular momentum vector associated with an atomic state can take up only certain specified directions in space. This concept of space quantization was shown by Otto Stern and Walthor Gerlach in their experiment.In the experiment, silver is vapourized in an electric oven and silver atoms spray into the evacuated apparatus through a small hole in the oven wall. The atoms which are electrically neutral but have a magnetic moment, are formed into a narrow beam as they pass through a slit in a screen. The beam, thus collimated, then passes between the poles of an electromagnet and finally, deposits its silver atoms on a glass plate that serves as a detector. The pole faces of the magnet are shaped to make the magnetic field as nonuniform as possible.In a non-uniform magnetic field, there is a net force on a magnetic dipole. Its magnitude and direction depends on the orientation of the dipole. Thus the silver atoms in the beam are deflected up or down, depending on the orientation of their magnetic dipole moments with respect to the z–direction.The potential energy of a magnetic dipole in a magnetic field where is magnetic dipole moment of the atom. From symmetry, the magnetic field at the beam position has no x or y components i.e.The net force Fz on the dipole isThus, the net force depends, not on the magnitude of the field itself, but on its spatial derivative or gradient.The ResultsIf space quantization did not exist, then could take on any value from + to –, the result would be a spreading out of the beam when the magnet was turned ON. However, the beam was split cleanly into two subbeams, each subbeam corresponding to one of the two permitted orientations of the magnetic moment ofthe silver atom, as shown.In a silver atom, all the spin and orbital magnetic moments of the electrons cancel, except for those of the atoms single valance electron. For this electron the orbital magnetic moment is zero because orbital angular momentum is zero (because for electrons of s–orbit, L = 0), leaving only the spin magnetic moment. This can take up only two orientations in a magnetic field, corresponding to ms = +1/2 and ms = – 1/2. Hence there are two subbeams – and not some other number.Q.A hydrogen atom in ground state passes through a magnetic field that has a gradient of 16mT/m in the vertical direction. If vertical component magnetic moment of the atom is 9.3 × 10–24 J/T, then force on it due to the magnetic moment of the electron is

The orbital and spin angular momentum of the atom influence its magnetic structure and these properties are most directly studied by placing the atom in a magnetic field. Also, a magnetic field can affect the wavelengths of the emitted photons.The angular momentum vector associated with an atomic state can take up only certain specified directions in space. This concept of space quantization was shown by Otto Stern and Walthor Gerlach in their experiment.In the experiment, silver is vapourized in an electric oven and silver atoms spray into the evacuated apparatus through a small hole in the oven wall. The atoms which are electrically neutral but have a magnetic moment, are formed into a narrow beam as they pass through a slit in a screen. The beam, thus collimated, then passes between the poles of an electromagnet and finally, deposits its silver atoms on a glass plate that serves as a detector. The pole faces of the magnet are shaped to make the magnetic field as nonuniform as possible.In a non-uniform magnetic field, there is a net force on a magnetic dipole. Its magnitude and direction depends on the orientation of the dipole. Thus the silver atoms in the beam are deflected up or down, depending on the orientation of their magnetic dipole moments with respect to the z–direction.The potential energy of a magnetic dipole in a magnetic field where is magnetic dipole moment of the atom. From symmetry, the magnetic field at the beam position has no x or y components i.e.The net force Fz on the dipole isThus, the net force depends, not on the magnitude of the field itself, but on its spatial derivative or gradient.The ResultsIf space quantization did not exist, then could take on any value from + to –, the result would be a spreading out of the beam when the magnet was turned ON. However, the beam was split cleanly into two subbeams, each subbeam corresponding to one of the two permitted orientations of the magnetic moment ofthe silver atom, as shown.In a silver atom, all the spin and orbital magnetic moments of the electrons cancel, except for those of the atoms single valance electron. For this electron the orbital magnetic moment is zero because orbital angular momentum is zero (because for electrons of s–orbit, L = 0), leaving only the spin magnetic moment. This can take up only two orientations in a magnetic field, corresponding to ms = +1/2 and ms = – 1/2. Hence there are two subbeams – and not some other number.Q.A hydrogen atom in ground state passes through a magnetic field that has a gradient of 16mT/m in the vertical direction. If vertical component magnetic moment of the atom is 9.3 × 10–24 J/T, then force on it due to the magnetic moment of the electron is

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An electric dipole of moment P is placed in a uniform electric field E,with P parallel to E. It is then rotated by an angle theta. The work done is?
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An electric dipole of moment P is placed in a uniform electric field E,with P parallel to E. It is then rotated by an angle theta. The work done is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An electric dipole of moment P is placed in a uniform electric field E,with P parallel to E. It is then rotated by an angle theta. The work done is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An electric dipole of moment P is placed in a uniform electric field E,with P parallel to E. It is then rotated by an angle theta. The work done is?.
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