Question

The diagram shows a wire loop that consists of two different-radius half-circles. Segment 1 has a larger radius than Segment 2, but both segments are centered on point P.
The segments are connected by straight wires as shown, and an unseen source of EMF creates a constant counterclockwise current in the wire.
Which wire segment creates a stronger magnetic field at point P?

• A. Segment 1 creates stronger magnetic field because Segment 1 is longer.
• B. Segment 2 creates stronger magnetic field because Segment 2 is closer.
• C. Both segments create the same strength magnetic field because both segments have the same angle.
• D. Both segments create the same strength magnetic field because both segments have the same current.

Answer 1

The correct option is B Segment 2 creates stronger magnetic field because Segment 2 is closer.

Magnetic field due to segment 1 at point P ,

$B_1=\frac{{\mu }_{0}I}{4R_1}$ (out of the page , by right hand thumb rule )

Magnetic field due to segment 2 at point P ,

$B_2=\frac{{\mu }_{0}I}{4R_2}$ (out of the page , by right hand thumb rule ) ,

now as given $R_1>R_2$ , therefore $B_2>B_1$