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An electric dipole is kept on the axis of a uniformly charge ring at distance R/root 2 from the centre of the ring. the direction of the dipole moment is along the axis. The dipole moment is P charge of the ring is Q and radius of the ring is R. The force on the dipole is nearly.?
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An electric dipole is kept on the axis of a uniformly charge ring at d...
**Introduction:**
In this problem, we are given an electric dipole on the axis of a uniformly charged ring. We need to find out the force acting on the dipole.
**Given:**
- Distance between the dipole and the centre of the ring = R/√2
- Dipole moment = P
- Charge of the ring = Q
- Radius of the ring = R
**Approach:**
- Find out the electric field at the point of the dipole due to the ring.
- Use the formula for the force on an electric dipole in an external electric field to find out the force acting on the dipole.
**Calculations:**
- Electric field at the point of the dipole due to the ring can be found using the formula for the electric field due to a uniformly charged ring.
E = kQ/√(R²+(R/√2)²)
- The direction of the electric field at the point of the dipole is along the axis of the ring.
- The electric field due to the ring at the point of the dipole can be written as the sum of the electric fields due to the charges of the ring. The electric field due to each charge of the ring at the point of the dipole can be written as
dE = kdq/((R/√2)²+x²)³/²
- The force on an electric dipole in an external electric field is given by the formula
F = PdE/dx
- Using this formula, we can find out the force acting on the dipole.
**Final Answer:**
The force acting on the dipole is given by the formula
F = kPQ(x/((R/√2)²+x²)³/²)
where x = R/√2
On substituting the values, we get
F = kPQ/(2√3R²)
Thus, the force acting on the dipole is proportional to the product of the dipole moment and the charge of the ring, and inversely proportional to the square of the radius of the ring.
In this problem, we are given an electric dipole on the axis of a uniformly charged ring. We need to find out the force acting on the dipole.
**Given:**
- Distance between the dipole and the centre of the ring = R/√2
- Dipole moment = P
- Charge of the ring = Q
- Radius of the ring = R
**Approach:**
- Find out the electric field at the point of the dipole due to the ring.
- Use the formula for the force on an electric dipole in an external electric field to find out the force acting on the dipole.
**Calculations:**
- Electric field at the point of the dipole due to the ring can be found using the formula for the electric field due to a uniformly charged ring.
E = kQ/√(R²+(R/√2)²)
- The direction of the electric field at the point of the dipole is along the axis of the ring.
- The electric field due to the ring at the point of the dipole can be written as the sum of the electric fields due to the charges of the ring. The electric field due to each charge of the ring at the point of the dipole can be written as
dE = kdq/((R/√2)²+x²)³/²
- The force on an electric dipole in an external electric field is given by the formula
F = PdE/dx
- Using this formula, we can find out the force acting on the dipole.
**Final Answer:**
The force acting on the dipole is given by the formula
F = kPQ(x/((R/√2)²+x²)³/²)
where x = R/√2
On substituting the values, we get
F = kPQ/(2√3R²)
Thus, the force acting on the dipole is proportional to the product of the dipole moment and the charge of the ring, and inversely proportional to the square of the radius of the ring.
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An electric dipole is kept on the axis of a uniformly charge ring at d...
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An electric dipole is kept on the axis of a uniformly charge ring at distance R/root 2 from the centre of the ring. the direction of the dipole moment is along the axis. The dipole moment is P charge of the ring is Q and radius of the ring is R. The force on the dipole is nearly.?
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An electric dipole is kept on the axis of a uniformly charge ring at distance R/root 2 from the centre of the ring. the direction of the dipole moment is along the axis. The dipole moment is P charge of the ring is Q and radius of the ring is R. The force on the dipole is nearly.? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about An electric dipole is kept on the axis of a uniformly charge ring at distance R/root 2 from the centre of the ring. the direction of the dipole moment is along the axis. The dipole moment is P charge of the ring is Q and radius of the ring is R. The force on the dipole is nearly.? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An electric dipole is kept on the axis of a uniformly charge ring at distance R/root 2 from the centre of the ring. the direction of the dipole moment is along the axis. The dipole moment is P charge of the ring is Q and radius of the ring is R. The force on the dipole is nearly.?.
An electric dipole is kept on the axis of a uniformly charge ring at distance R/root 2 from the centre of the ring. the direction of the dipole moment is along the axis. The dipole moment is P charge of the ring is Q and radius of the ring is R. The force on the dipole is nearly.? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about An electric dipole is kept on the axis of a uniformly charge ring at distance R/root 2 from the centre of the ring. the direction of the dipole moment is along the axis. The dipole moment is P charge of the ring is Q and radius of the ring is R. The force on the dipole is nearly.? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An electric dipole is kept on the axis of a uniformly charge ring at distance R/root 2 from the centre of the ring. the direction of the dipole moment is along the axis. The dipole moment is P charge of the ring is Q and radius of the ring is R. The force on the dipole is nearly.?.
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