Question

The diagram shows a wire that is bent into a loop consisting of two straight segments 2 and 4 and two quarter-circular segments 1 and 3. Point P is at the curvature center of the curved segments and is collinear to segments 2 and 4. An unseen source of EMF causes a constant clockwise current to exist in the wire loop.
Which segments create a magnetic field at point P, and what is the direction of the fields that are created at point P?

• A. Segment 1 creates magnetic field directed into the page, and Segment 3 creates magnetic field directed out of the page.
• B. Segment 1 creates magnetic field directed out of the page, and Segment 3 creates magnetic field directed into the page.
• C. Segment 2 creates magnetic field directed into the page, and Segment 4 creates magnetic field directed out of the page.
• D. Segment 2 creates magnetic field directed out of the page, and Segment 4 creates magnetic field directed into the page.

Answer 1

The correct option is A Segment 1 creates magnetic field directed into the page, and Segment 3 creates magnetic field directed out of the page.

According to Biot-Savart's law the magnetic field due to a current carrying wire is given by ,

$dB=\frac{{\mu }_0}{4\pi }.\frac{Idl\sin \theta }{r^2}$ ,

in the given diagram , for segment 2 and 4 ,

$\theta =0^{o}or{180}^o$ ,

therefore magnetic field $dB=0$

now as the segment 1 and 3 have value of $\theta$ ,other than $0$ or $180$ therefore they will create magnetic fields at point P , whose directions will be given by Right hand thumb rule ,

for segment 1 - magnetic field will be directed into the page

for segment 3 - magnetic field will be directed out of the page .