Effect of Changing Magnetic Field on Flux through a Coil

[cse63146]

Homework Statement

You hold a wire coil perpendicular to a magnetic field B. If the magnitude of B increases while its direction remains unchanged, how will the magnetic flux through the coil change?

Check all that apply:

The flux is unchanged because the position of the coil with respect to B is unchanged.
The flux increases because the magnitude of B increases.
The flux decreases because the magnitude of B increases.
The flux is unchanged because the surface area of the coil is unchanged.

Homework Equations

$$A_{eff} = Acos\vartheta$$

The Attempt at a Solution

According to the formula - $$A_{eff} = Acos\vartheta$$, the magnetic flux is determined by the area. I believe the answer is "flux is unchanged because the surface area of the coil is unchanged" since in the problem, only B is changing.

Am I right?

 

[rock.freak667]

Magnetic flux linkage is given by:

$$\Phi =BAcos\theta$$

 

[cse63146]

Ah, since magnetic filed is directly proportional to the magnetic flux, it would make the solution - The flux increases because the magnitude of B increases, correct?

 

[rock.freak667]

Ah, since magnetic filed is directly proportional to the magnetic flux, it would make the solution - The flux increases because the magnitude of B increases, correct?

Correct.

 

[cse63146]

Thanks, but another question "unlocked" itself after I finished the first one:

If B is kept constant but the coil is rotated so that it is parallel to B, how will the magnetic flux through the coil vary?

The flux is unchanged because the magnitude of B is constant.
The flux increases because the angle between B and the coil's axis changes.
The flux decreases because the angle between B and the coil's axis changes.
The flux is unchanged because the area of the coil is unchanged.

So $$\Phi = ABcos\vartheta$$ and since the coil is parallel to B, it means $$\vartheta0$$ and $$cos\vartheta = 1$$ so in this case $$\Phi = AB$$ and since B is constant and so is A, there are two answers:

i) The flux is unchanged because the magnitude of B is constant.
ii) The flux is unchanged because the area of the coil is unchanged.

Correct?

 

[cse63146]

can someone just double check me reasoning/answer, as this is the last question on my assigment.

Thank You.

 

[Snazzy]

When the coil is perpendicular:
$$\theta=0$$

When the coil is parallel, the tilt is 90 degrees, and the magnetic flux is 0. You can imagine flux as the number of field lines passing through the area. If the coil is parallel to the magnetic field, none of the field lines get passed the area bounded by the coil.

 

[cse63146]

Since it's being rotated so it would be parallel, $$\vartheta$$ is decreasing so the answer is:

The flux decreases because the angle between B and the coil's axis changes. Correct?

 

[Snazzy]

Yes.

 

[cse63146]

Thank you both for all your help.