In the circuit shown below, a current 3I enters at A. The semicircular parts ABC and ADC have equal radii 'r' but resistances 2R and R respectively. The magnetic field at the center of the circular loop ABCD is __________.

Fill in the blank with the correct answer from the options given below:

$\frac{\mu_0 I}{4 r}$ out of the plane

The current through part ABC is I and current through ADC is 2I.

Magnetic field at the centre due to ABC is $ B_1 = \frac{\mu_0 I}{4r}$ In to the plane.

Magnetic field at the centre due to ADC is $ B_2 = \frac{2\mu_0 I}{4r}$ out of the plane.

Net magnetic field is $B = B_2 - B_1 = \frac{\mu_0 I}{4r}$ out of the plane.

The correct answer is Option (1) → $\frac{\mu_0 I}{4 r}$ out of the plane