Question:
Assertion (A): When a circular coil, placed in a region with its plane parallel to a magnetic field, expands radially outwards, no emf is induced in it.
Reason (R): There is a constant magnetic field in the perpendicular (to the plane of the coil) direction.
Assertion (A): When a circular coil, placed in a region with its plane parallel to a magnetic field, expands radially outwards, no emf is induced in it.
Reason (R): There is a constant magnetic field in the perpendicular (to the plane of the coil) direction.
Show Hint
Magnetic flux through a coil is
\[
\Phi=BA\cos\theta,
\]
where \(\theta\) is the angle between the magnetic field and the area vector. If the magnetic field lies in the plane of the coil, then \(\theta=90^\circ\) and the flux is always zero.
Updated On: Jun 26, 2026
- Both (A) and (R) are true. (R) is the correct explanation of (A).
- Both (A) and (R) are true. (R) is not the correct explanation of (A).
- (A) is true, (R) is false.
- (A) is false, (R) is true.
Show Solution
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The Correct Option is C
Solution and Explanation
Step 1: Analyze the Assertion (A).
The plane of the circular coil is parallel to the magnetic field.
Therefore, the magnetic field is along the plane of the coil and makes an angle \[ \theta=90^\circ \] with the area vector of the coil.
The magnetic flux through the coil is \[ \Phi=BA\cos\theta. \] Substituting \[ \theta=90^\circ, \] we get \[ \Phi=BA\cos90^\circ=0. \] Since the magnetic flux is always zero, even if the radius and area of the coil change, \[ \frac{d\Phi}{dt}=0. \] Hence, \[ \mathcal{E}=-\frac{d\Phi}{dt}=0. \] Therefore, no emf is induced.
Thus, Assertion (A) is true.
Step 2: Analyze the Reason (R).
The reason states that there is a constant magnetic field in the direction perpendicular to the plane of the coil.
This statement is incorrect.
The problem clearly states that the plane of the coil is parallel to the magnetic field. Hence, the magnetic field lies in the plane of the coil, not perpendicular to it.
Therefore, Reason (R) is false.
Step 3: Final conclusion.
Assertion (A) is true, but Reason (R) is false.
Hence, \[ \boxed{\text{(A) is true, (R) is false}} \] Therefore, the correct option is \[ \boxed{(3)} \]
The plane of the circular coil is parallel to the magnetic field.
Therefore, the magnetic field is along the plane of the coil and makes an angle \[ \theta=90^\circ \] with the area vector of the coil.
The magnetic flux through the coil is \[ \Phi=BA\cos\theta. \] Substituting \[ \theta=90^\circ, \] we get \[ \Phi=BA\cos90^\circ=0. \] Since the magnetic flux is always zero, even if the radius and area of the coil change, \[ \frac{d\Phi}{dt}=0. \] Hence, \[ \mathcal{E}=-\frac{d\Phi}{dt}=0. \] Therefore, no emf is induced.
Thus, Assertion (A) is true.
Step 2: Analyze the Reason (R).
The reason states that there is a constant magnetic field in the direction perpendicular to the plane of the coil.
This statement is incorrect.
The problem clearly states that the plane of the coil is parallel to the magnetic field. Hence, the magnetic field lies in the plane of the coil, not perpendicular to it.
Therefore, Reason (R) is false.
Step 3: Final conclusion.
Assertion (A) is true, but Reason (R) is false.
Hence, \[ \boxed{\text{(A) is true, (R) is false}} \] Therefore, the correct option is \[ \boxed{(3)} \]
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