Question

A current carrying loop is placed in a uniform magnetic field pointing in negative z direction. Branch PQRS is a tree quarter circle, while branch PS is straight. If force on branch PS is F, force on branch PQR is:

• A. $\sqrt{2}F$
• B. $\frac{F}{\sqrt{2}}$
• C. $\frac{\pi F}{\sqrt{2}}$
• D. $\sqrt{2}\pi F$

Answer 1

The correct option is A $\sqrt{2}F$

$\overrightarrow{F_m}=i(\overrightarrow{l}\times \overrightarrow{B})F_m=ilB\therefore F_{PS}=i\left(\sqrt{2}R\right)B=\sqrt{2}iRB=F{F}_{PQR}=i\left(PR\right)B=i.2R.B=2iRB\therefore F_{PQR}=\sqrt{2}F$