Question:
An infinitely long solenoid of radius \( r \) and number of turns per unit length \( n \) carries a steady current \( I \). The ratio of the magnetic fields at a point on the axis of the solenoid to a point \( r/2 \) from the axis is ..............
An infinitely long solenoid of radius \( r \) and number of turns per unit length \( n \) carries a steady current \( I \). The ratio of the magnetic fields at a point on the axis of the solenoid to a point \( r/2 \) from the axis is ..............
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Magnetic field strength decreases with the square of the distance from the solenoid. The field is strongest at the center of the solenoid.
Updated On: Dec 11, 2025
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Correct Answer: 1
Solution and Explanation
Step 1: Magnetic field inside a solenoid.
The magnetic field inside a long solenoid is given by: \[ B = \mu_0 n I \] where \( \mu_0 \) is the permeability of free space, \( n \) is the number of turns per unit length, and \( I \) is the current.
Step 2: Magnetic field outside a solenoid.
The magnetic field outside a solenoid decreases with distance from the solenoid. The ratio of the magnetic field at a point on the axis of the solenoid to a point \( r/2 \) from the axis is proportional to the inverse of the distance. Thus, the ratio is \( 4 \).
Step 3: Conclusion.
The ratio of the magnetic fields is 4.
The magnetic field inside a long solenoid is given by: \[ B = \mu_0 n I \] where \( \mu_0 \) is the permeability of free space, \( n \) is the number of turns per unit length, and \( I \) is the current.
Step 2: Magnetic field outside a solenoid.
The magnetic field outside a solenoid decreases with distance from the solenoid. The ratio of the magnetic field at a point on the axis of the solenoid to a point \( r/2 \) from the axis is proportional to the inverse of the distance. Thus, the ratio is \( 4 \).
Step 3: Conclusion.
The ratio of the magnetic fields is 4.
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