Magnetic flux through a coil

Magnetic flux is given by $\Phi = BA\cos\theta$ where:

• $B$ = magnetic field magnitude
• $A$ = area of the coil
• $\theta$ = angle between the magnetic field and the normal to the plane of the coil.

Since the question mentions the angle between magnetic field and plane of coil, if that angle is $\alpha$, then $\theta = 90^\circ - \alpha$ so flux may also be written as $\Phi = BA\sin\alpha$

Initial condition

The plane of the coil is perpendicular to the magnetic field.

That means the magnetic field is along the normal to the coil, so $\theta = 0^\circ$ and initially $\Phi = BA$

Check each statement

A. By changing the magnitude of the magnetic field within the coil

Since $\Phi = BA\cos\theta$ changing $B$ changes $\Phi$.

So, A is correct.

B. By changing the area of coil within the magnetic field

Flux depends on area $A$. If area changes, flux changes.

So, B is correct.

C. By changing the angle between the direction of magnetic field and the plane of the coil

Flux depends on orientation. Changing the angle changes $\theta$ (or equivalently $\alpha$), hence changes flux.

So, C is correct.

D. By reversing the magnetic field direction abruptly without changing its magnitude

Reversing the field direction changes $\theta$ from $0^\circ$ to $180^\circ$. Then flux changes from $\Phi_i = BA\cos 0^\circ = BA$ to $\Phi_f = BA\cos 180^\circ = -BA$ Thus magnetic flux changes.

So, D is also correct.

Conclusion

All four statements $A, B, C,$ and $D$ can change the magnetic flux through the coil.

But among the given options, there is no option containing all four. Hence the listed options are incomplete/inconsistent.

Comparison with stored answer

The stored correct answer is B: A, B and C only.

However, statement D is also correct because reversing magnetic field direction changes flux from $+BA$ to $-BA$.

Therefore, I do not agree with the stored answer.