A coil is placed in magnetic field such that plane of coil is perpendicular to the direction of magnetic field. The magnetic flux through a coil can be changed :
A. By changing the magnitude of the magnetic field within the coil
B. By changing the area of coil within the magnetic field
C. By changing the angle between the direction of magnetic field and the plane of the coil
D. By reversing the magnetic field direction abruptly without changing its magnitude.
Choose the most appropriate answer from the options given below :
A coil is placed in magnetic field such that plane of coil is perpendicular to the direction of magnetic field. The magnetic flux through a coil can be changed :
A. By changing the magnitude of the magnetic field within the coil
B. By changing the area of coil within the magnetic field
C. By changing the angle between the direction of magnetic field and the plane of the coil
D. By reversing the magnetic field direction abruptly without changing its magnitude.
Choose the most appropriate answer from the options given below :
Show Hint
Understand the formula for magnetic flux and how each variable (B, A, and θ) affects the flux. Consider the dot product and its geometrical interpretation.
- A and C only
- A, B and C only
- A, B and D only
- A and B only
The Correct Option is B
Approach Solution - 1
Step 1: Recall the Formula for Magnetic Flux
The magnetic flux (\(\Phi\)) through a coil is given by:
\[ \Phi = \vec{B} \cdot \vec{A} = BA \cos \theta \]
where \(B\) is the magnetic field strength, \(A\) is the area of the coil, and \(\theta\) is the angle between the magnetic field vector and the area vector (which is perpendicular to the plane of the coil).
Step 2: Analyze Each Option
A: Changing the magnitude of the magnetic field (\(B\)) directly affects the magnetic flux (\(\Phi\)). So, A is correct.
B: Changing the area of the coil (\(A\)) within the magnetic field also directly affects the magnetic flux (\(\Phi\)). So, B is correct.
C: Changing the angle (\(\theta\)) between the magnetic field and the plane of the coil changes \(\cos \theta\) and thus the magnetic flux (\(\Phi\)). So, C is correct.
D: Reversing the magnetic field direction means changing the direction of \(\vec{B}\) by 180 degrees. This means that \(\theta\) becomes \(\theta + 180^\circ\).
\[ \cos(\theta + 180^\circ) = -\cos \theta, \]
meaning the flux reverses sign, but its magnitude changes. So, D is a way to change the flux.
Conclusion: Options A, B, and C are correct ways to change the magnetic flux, and D is also a way to change the magnetic flux. Because the question asks for the most appropriate answer, and D implies a change in magnitude, ABC is slightly preferred. So, option (2) is the most appropriate answer.
Approach Solution -2
ϕ=B⋅A
=BA⋅cosθ
Most suitable ans is B [Otherwise ABCD]
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Concepts Used:
Electromagnetic Induction
Electromagnetic Induction is a current produced by the voltage production due to a changing magnetic field. This happens in one of the two conditions:-
- When we place the conductor in a changing magnetic field.
- When the conductor constantly moves in a stationary field.
Formula:
The electromagnetic induction is mathematically represented as:-
e=N × d∅.dt
Where
- e = induced voltage
- N = number of turns in the coil
- Φ = Magnetic flux (This is the amount of magnetic field present on the surface)
- t = time
Applications of Electromagnetic Induction
- Electromagnetic induction in AC generator
- Electrical Transformers
- Magnetic Flow Meter