A rigid wire consists of a semicircular portion of radius $$R$$ and two straight sections. The wire is partially immerged in a perpendicular magnetic field $$B=B_0 \hat{k}$$ as shown in figure. The magnetic force on the wire if it has a current $$i$$ is:

Two insulated circular loop A and B of radius '$$a$$' carrying a current of '$$\mathrm{I}$$' in the anti clockwise direction as shown in the figure. The magnitude of the magnetic induction at the centre will be :

Two particles $$X$$ and $$Y$$ having equal charges are being accelerated through the same potential difference. Thereafter they enter normally in a region of uniform magnetic field and describes circular paths of radii $$R_1$$ and $$R_2$$ respectively. The mass ratio of $$X$$ and $$Y$$ is :

A proton moving with a constant velocity passes through a region of space without any change in its velocity. If $$\overrightarrow{\mathrm{E}}$$ and $$\overrightarrow{\mathrm{B}}$$ represent the electric and magnetic fields respectively, then the region of space may have :

(A) $$\mathrm{E}=0, \mathrm{~B}=0$$

(B) $$\mathrm{E}=0, \mathrm{~B} \neq 0$$

(C) $$\mathrm{E} \neq 0, \mathrm{~B}=0$$

(D) $$\mathrm{E} \neq 0, \mathrm{~B} \neq 0$$

Choose the most appropriate answer from the options given below :