Concept explainers
(a)
To explain: The effect on magnetic field inside a long solenoid for the given changes.
(a)
Explanation of Solution
Given:
The magnetic field inside a long solenoid is B .
The diameter of all the loops is doubled.
Formula used:
The magnetic field B inside a solenoid is given by,
Where
The magnetic field B inside a solenoid does not depend on the diameter of the loops of the solenoid. So any change in the diameter of the loops does not affect the magnetic field inside the solenoid.
Conclusion:
If the diameter of all the loops is doubled then the magnetic field inside the solenoid remains unchanged.
(b)
To explain: The effect on magnetic field inside a long solenoid for the given changes.
(b)
Explanation of Solution
Given:
The magnetic field inside a long solenoid is B .
The spacing between the loops is doubled.
Formula used:
Calculation:
The magnetic field inside a solenoid depends on the length of the solenoid. If the spacing between the loops of the solenoid is increased then the length of the solenoid increases and hence the magnetic field decreases. If the spacing between the loops gets doubled then the length of the solenoid gets doubled. Let the new length and the new magnetic field be
Conclusion:
If the spacing between the loops of a solenoid gets doubled, the magnetic field inside the solenoid gets reduced to half.
(c)
To explain: The effect on magnetic field inside a long solenoid for the given changes.
(c)
Explanation of Solution
Given:
The magnetic field inside a long solenoid is B .
The length of solenoid and number of loops are doubled.
Formula used:
Calculation:
The magnetic field inside a solenoid is inversely proportional to the length of the solenoid and proportional to the number of loops, so any change in either the number of loops or the length results in a change in the magnetic field.
Let
Let
Conclusion:
If both the length as well as the number of loops of a solenoid gets doubled, the magnetic field inside the solenoid does not change.
Chapter 20 Solutions
Physics: Principles with Applications
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