Six parallel infinite wires are placed at the vertices of a regular hexagon. Five wires carry current $I_0$ each while the sixth wire carries current $4I_0$ as shown. The resultant magnetic field at the centre of the hexagon is

A current / flows in a long straight wire with crosssection having the form of a thin quarter-ring of radius $R$ (see figure). The magnetic field $\overrightarrow{B}$ at point $O$ if the current flows out of the page is

A semicircular wire of radius $R$ carrying current $/$ is placed in a magnetic field as shown in the figure. On right hand side of  $yy\text{'}$ the magnetic field is $2B_0,$ outward and on the left hand side it is $B_0$ inward as shown. The magnetic force experience by the wire is

The magnetic field at the centre of dotted circle in the arrangement shown is

The magnetic field at point $P$ in the hollow cylindrical wire carrying a current $i$ shown in the figure at a distance $r$ from axis $(a<r<b)$ is given by (Taking current density to be uniform across its cross-section)

In the plane of coil a uniform magnetic field $B$ exists. Torque on the current carrying coil of radius $R$ is

Calculate the torque acting upon the following structure carrying current $/$ due to the magnetic field $B.$ Both the magnetic field and the structure are in the plane of paper as shown.

An infinite semi-cylindrical conducting shell of radius $R$ carrying a current $I$ along$-z$ direction as shown in figure. If a charge particle $(q, m)$ is projected from point $O$ (on the axis of semi-cylindrical shell) with velocity $\overrightarrow{v}=v_0\hat{j},$ then force on this charge particle will be

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