Some magnetic flux is changed from a coil of resistance 10 ohm. As a result an induced
current is developed in it, which varies with time as shown in figure. The magnitude of
change in flux through the coil in webers is:
Two coils are at fixed locations. When coil 1 has no current and the current in coil 2 increases at the rate 15.0 A/s the emf in coil 1 in 25.0 mV, when coil 2 has no current and coil 1 has a current of 3.6 A, the flux linkage in coil 2 is:
Based on the problem in your editor, here is the solution in 3 lines without using the $ symbol:
Find Mutual Inductance (M): M = Induced EMF / (rate of change of current) = 25.0 mV / 15.0 A/s = 1.667 mH.
Calculate Flux Linkage: Flux = M × Current = 1.667 mH × 3.6 A = 6.00 mWb.
Result: The flux linkage in coil 2 is 6.00 mWb (Option 4).
A flux of \(10^{-3}\text{ Wb}\) passes through a strip having an area \(A = 0.02\text{ m}^2\). The plane of the strip is at an angle of \(60^\circ\) to the direction of a uniform field \(B\). The value of \(B\) is:
The magnetic flux through the surface is given by \(\phi = B A \sin\theta\). Substituting \(\phi = 10^{-3}\text{ Wb}\), \(A = 0.02\text{ m}^2\), and \(\theta = 60^\circ\), we get \(B = \frac{10^{-3}}{0.02 \times \sin 60^\circ} \approx 0.058\text{ T}\).
Assertion (A): A changing magnetic flux induces an electric field.
Reason (R): An inductor always tends to keep the flux constant.
Faraday's Law states a changing magnetic flux induces an electric field. Inductors oppose change in flux, but don't keep it constant. Hence, Assertion is true and Reason is false.
Assertion (A): Magnetic flux is a vector quantity.
Reason (R): Value of magnetic flux cannot be negative.
Magnetic flux \(\phi = \vec{B} \cdot \vec{A}\) is a scalar quantity (A is false). Also, \(\phi = BA cos\theta\) can be negative when \(cos\theta\) is negative, indicating direction relative to area normal (R is false). Both are false.