Directions: In the following questions, a statement of assertion (A) ...
The magnetic field inside a solenoid is proportional to both the applied current and the number of turns per unit length. There is no dependence on the diameter of the solenoid, and the field strength doesn't depend on the position inside the solenoid, i.e., the field inside is constant.
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Directions: In the following questions, a statement of assertion (A) ...
Assertion: The magnitude of the magnetic field at a point on the axis of a current-carrying solenoid is inversely proportional to the current flowing through the solenoid.
Reason: The magnitude of the magnetic field at a point on the axis of a current-carrying solenoid is directly proportional to the number of turns per unit length of the solenoid.
To understand why the correct answer is option D, let's break down the assertion and reason separately:
Assertion (A): The magnitude of the magnetic field at a point on the axis of a current-carrying solenoid is inversely proportional to the current flowing through the solenoid.
Reason (R): The magnitude of the magnetic field at a point on the axis of a current-carrying solenoid is directly proportional to the number of turns per unit length of the solenoid.
Explanation:
1. The magnetic field produced by a solenoid is given by the equation B = μ₀nI, where B is the magnetic field, μ₀ is the permeability of free space, n is the number of turns per unit length, and I is the current flowing through the solenoid.
2. From the equation, it is clear that the magnetic field is directly proportional to the current flowing through the solenoid (I). Therefore, the reason (R) is correct.
3. However, the assertion (A) states that the magnitude of the magnetic field is inversely proportional to the current flowing through the solenoid. This is incorrect as the magnitude of the magnetic field is directly proportional to the current flowing through the solenoid.
4. Therefore, the assertion (A) is false.
5. Since the assertion (A) is false, and the reason (R) is true, the correct answer is option D - Assertion (A) is false but reason (R) is true.
In summary, the magnitude of the magnetic field at a point on the axis of a current-carrying solenoid is directly proportional to the current flowing through the solenoid and the number of turns per unit length of the solenoid. The assertion incorrectly states an inverse relationship between the magnetic field and the current, while the reason correctly states the direct relationship between the magnetic field and the number of turns per unit length.
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