Question

In the loops shown in figure, all curved sections are either simicircles or quarter circles. all the loops carry same current. The magnetic fields at the center have magnitudes $B_1,B_2,B_3,B_4$. Then,

• A. $B_4$ is maximum
• B. $B_3$ is minimum
• C. $B_4>B_1>B_2>B_3$
• D. $B_1>B_4>B_3>B_2$

Answer 1

Answer: (A), (B), (C)

The correct options are
A $B_4$ is maximum
B $B_3$ is minimum
C $B_4>B_1>B_2>B_3$

If a current passes through any conductor,net charge through any section is zero. hence, electric field in the vicinity of the conductor is zero. We can observe using Biot and Sarvat law that the magnetic field at the axis of the cylindrical wire will be zero. Electric field at the axis of the wire cannot be zero otherwise the current through the wire cannot flow.

For B1 and B4, the contribution due to the different sections add up. For B2 and B3, the contributions due to the outer sections oppose the contributions due to inner sections. Thus, B1 and B4 are greater than B2 and B3. For B4, there is a section with radius <b and hence, it contributes more than the semicircular section of radius b for B1. Thus B4>B1.
For B3, there is a section with radius >b and hence it contributes less than the semicircular section of radius b for B2. Thus B3<B2, Hence B4>B1>B2>B3