1. Given data

• Two magnetic fields, $\vec B_1$ and $\vec B_2$, are inclined at an angle of $75^\circ$.
• $B_1 = 15\,\text{mT}$.
• The magnetic dipole is in stable equilibrium at an angle of $30^\circ$ with $\vec B_1$.

We need the magnitude of $B_2$.

2. Condition for stable equilibrium

A magnetic dipole in equilibrium aligns along the resultant magnetic field.

So if the dipole makes an angle of $30^\circ$ with $\vec B_1$, then the resultant field $\vec B_R$ must also make an angle of $30^\circ$ with $\vec B_1$.

Since $\vec B_2$ is at $75^\circ$ to $\vec B_1$, resolve along and perpendicular to $\vec B_1$.

3. Resolve the fields

Take $\vec B_1$ along the $x$-axis.

Then:

and

Hence the resultant is

Since $\vec B_R$ makes angle $30^\circ$ with $\vec B_1$ (the $x$-axis),

4. Substitute trigonometric values

So,

Multiply through:

Using $\sqrt{3} \approx 1.732$,

5. Closest option

So the correct option is A.

6. Comparison with stored answer

Stored correct answer: A

Our derived answer: A

They agree.