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A battery is connected between two points A and B on the circumference of a uniform conducting ring of radius r and resistance R. One of the arcs AB of the ring subtends an angle θ at the centre. The value of, the magnetic induction at the centre due to the current in the ring is?
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A battery is connected between two points A and B on the circumference...
Introduction
When a battery is connected between two points A and B on a uniform conducting ring, it creates a current that flows through the ring. The magnetic field at the center of the ring can be calculated using Ampère's law and the Biot-Savart law.
Magnetic Field Due to a Current-Carrying Ring
- The total current \(I\) flowing through the ring is given by Ohm's law:
\[
I = \frac{V}{R}
\]
where \(V\) is the voltage of the battery and \(R\) is the total resistance of the ring.
- The arc AB subtends an angle \(\theta\) at the center. The fraction of the total circular loop corresponding to this angle is:
\[
\frac{\theta}{2\pi}
\]
- Therefore, the effective length of the arc AB is:
\[
L = r\theta
\]
Magnetic Induction at the Center
- The magnetic field at the center of the ring due to the entire loop can be expressed as:
\[
B = \frac{\mu_0 I}{2r}
\]
where \(\mu_0\) is the permeability of free space.
- For the arc AB, the magnetic induction can be calculated as:
\[
B_{AB} = \frac{\mu_0 I}{4\pi r} \cdot \theta
\]
- Substituting \(I\) from Ohm’s law:
\[
B_{AB} = \frac{\mu_0 V \theta}{4\pi R r}
\]
Conclusion
Thus, the magnetic induction at the center of the conducting ring due to the current is:
\[
B = \frac{\mu_0 V \theta}{4\pi R r}
\]
This equation encapsulates the relationship between the induced magnetic field, voltage, resistance, and the geometry of the ring.
When a battery is connected between two points A and B on a uniform conducting ring, it creates a current that flows through the ring. The magnetic field at the center of the ring can be calculated using Ampère's law and the Biot-Savart law.
Magnetic Field Due to a Current-Carrying Ring
- The total current \(I\) flowing through the ring is given by Ohm's law:
\[
I = \frac{V}{R}
\]
where \(V\) is the voltage of the battery and \(R\) is the total resistance of the ring.
- The arc AB subtends an angle \(\theta\) at the center. The fraction of the total circular loop corresponding to this angle is:
\[
\frac{\theta}{2\pi}
\]
- Therefore, the effective length of the arc AB is:
\[
L = r\theta
\]
Magnetic Induction at the Center
- The magnetic field at the center of the ring due to the entire loop can be expressed as:
\[
B = \frac{\mu_0 I}{2r}
\]
where \(\mu_0\) is the permeability of free space.
- For the arc AB, the magnetic induction can be calculated as:
\[
B_{AB} = \frac{\mu_0 I}{4\pi r} \cdot \theta
\]
- Substituting \(I\) from Ohm’s law:
\[
B_{AB} = \frac{\mu_0 V \theta}{4\pi R r}
\]
Conclusion
Thus, the magnetic induction at the center of the conducting ring due to the current is:
\[
B = \frac{\mu_0 V \theta}{4\pi R r}
\]
This equation encapsulates the relationship between the induced magnetic field, voltage, resistance, and the geometry of the ring.
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A battery is connected between two points A and B on the circumference of a uniform conducting ring of radius r and resistance R. One of the arcs AB of the ring subtends an angle θ at the centre. The value of, the magnetic induction at the centre due to the current in the ring is?
Question Description
A battery is connected between two points A and B on the circumference of a uniform conducting ring of radius r and resistance R. One of the arcs AB of the ring subtends an angle θ at the centre. The value of, the magnetic induction at the centre due to the current in the ring is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A battery is connected between two points A and B on the circumference of a uniform conducting ring of radius r and resistance R. One of the arcs AB of the ring subtends an angle θ at the centre. The value of, the magnetic induction at the centre due to the current in the ring is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A battery is connected between two points A and B on the circumference of a uniform conducting ring of radius r and resistance R. One of the arcs AB of the ring subtends an angle θ at the centre. The value of, the magnetic induction at the centre due to the current in the ring is?.
A battery is connected between two points A and B on the circumference of a uniform conducting ring of radius r and resistance R. One of the arcs AB of the ring subtends an angle θ at the centre. The value of, the magnetic induction at the centre due to the current in the ring is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A battery is connected between two points A and B on the circumference of a uniform conducting ring of radius r and resistance R. One of the arcs AB of the ring subtends an angle θ at the centre. The value of, the magnetic induction at the centre due to the current in the ring is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A battery is connected between two points A and B on the circumference of a uniform conducting ring of radius r and resistance R. One of the arcs AB of the ring subtends an angle θ at the centre. The value of, the magnetic induction at the centre due to the current in the ring is?.
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