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A long solenoid carrying a current produces a magnetic field B along its axis. If the current is doubled and the number of turns per cm is halved, the new value of magnetic field will be equal to
- a)B
- b)2B
- c)4B
- d)B/2
Correct answer is option 'A'. Can you explain this answer?
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A long solenoid carrying a current produces a magnetic field B along i...
The given question is related to the magnetic field produced by a long solenoid carrying a current. Let's analyze the situation step-by-step to understand why the correct answer is option 'A' - B.
1. Magnetic Field Produced by a Solenoid:
A solenoid is a long coil of wire, typically wound in a helical shape. When a current flows through the solenoid, it produces a magnetic field along its axis. This magnetic field is proportional to the current flowing through the solenoid and the number of turns per unit length.
2. Effect of Doubling the Current:
When the current flowing through the solenoid is doubled, the magnetic field produced by the solenoid also doubles. This is because the magnetic field is directly proportional to the current.
3. Effect of Halving the Number of Turns per cm:
When the number of turns per cm is halved, the magnetic field produced by each turn is also halved. This is because the magnetic field is directly proportional to the number of turns per unit length.
4. Calculation of the New Magnetic Field:
In the given scenario, the current is doubled and the number of turns per cm is halved. Therefore, the change in the magnetic field can be calculated as follows:
Change in magnetic field = (Change in current) * (Change in number of turns per cm)
Change in magnetic field = (2 * B) * (0.5 * B)
Change in magnetic field = B^2
Therefore, the new magnetic field is equal to B.
5. Conclusion:
From the above analysis, it can be concluded that when the current is doubled and the number of turns per cm is halved, the new value of the magnetic field remains the same as the original value, which is B. Hence, the correct answer is option 'A' - B.
1. Magnetic Field Produced by a Solenoid:
A solenoid is a long coil of wire, typically wound in a helical shape. When a current flows through the solenoid, it produces a magnetic field along its axis. This magnetic field is proportional to the current flowing through the solenoid and the number of turns per unit length.
2. Effect of Doubling the Current:
When the current flowing through the solenoid is doubled, the magnetic field produced by the solenoid also doubles. This is because the magnetic field is directly proportional to the current.
3. Effect of Halving the Number of Turns per cm:
When the number of turns per cm is halved, the magnetic field produced by each turn is also halved. This is because the magnetic field is directly proportional to the number of turns per unit length.
4. Calculation of the New Magnetic Field:
In the given scenario, the current is doubled and the number of turns per cm is halved. Therefore, the change in the magnetic field can be calculated as follows:
Change in magnetic field = (Change in current) * (Change in number of turns per cm)
Change in magnetic field = (2 * B) * (0.5 * B)
Change in magnetic field = B^2
Therefore, the new magnetic field is equal to B.
5. Conclusion:
From the above analysis, it can be concluded that when the current is doubled and the number of turns per cm is halved, the new value of the magnetic field remains the same as the original value, which is B. Hence, the correct answer is option 'A' - B.
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Community Answer
A long solenoid carrying a current produces a magnetic field B along i...
B = μ0ni
Now i → 2i
And n → n/2
Now i → 2i
And n → n/2
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A long solenoid carrying a current produces a magnetic field B along its axis. If the current is doubled and the number of turns per cm is halved, the new value of magnetic field will be equal toa)Bb)2Bc)4Bd)B/2Correct answer is option 'A'. Can you explain this answer?
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