A charge particle $\left(\frac{\mathrm{q}}{\mathrm{m}}=1 \mathrm{in} \mathrm{S}.\mathrm{I}. \mathrm{unit}\right)$ is projected at $t=0$ with velocity $5\sqrt{2} \mathrm{m} {\mathrm{s}}^{-1}$ at an angle of $45°$ with $+x$ direction as shown in a region where uniform magnetic field $\overrightarrow{B}=\left(-\frac{\hat{i}}{\sqrt{2}}+\frac{\hat{j}}{\sqrt{2}}\right) T$  exist. Velocity of charge particle at $t=\frac{\pi }{4} \mathrm{s}$ will be

A charge particle $(q=1\mathrm{C}, m=1 \mathrm{kg})$ moving with velocity $\overrightarrow{v}=5\hat{i} \mathrm{m} {\mathrm{s}}^{-1}$ passes through a region of width $\left(D=\frac{3}{2} \mathrm{m}\right)$ where uniform magnetic field $\overrightarrow{B}=-2\hat{k} \mathrm{T}$ exist as shown. Find average force exerted by magnetic field on this charge particle.

The figure shows three long straight current carrying conductors. The straight parts are long and the circular part in each case in ${\left(\frac{3}{4}\right)}^{\text{th }}$ of a complete circle. Let $B_a, B_b$ and $B_c$ represents the strength of field at the centre $O$ in the three cases, then

Two thick wires and two thin wires, all of same material and same length form a square in the three different ways $P, Q$ and $R$ as shown. The current flowing through the arrangement is $i.$ Let $B_P, B_Q$ and $B_R$ represent the magnetic field at the centre of squares in the three cases, then

The figure shows two infinite parallel sheets of current, with current per unit length ${\lambda }_1$ and ${\lambda }_2.$ If $B_P,$ $B_Q$ and $B_R$ represent the magnetic field at the points $P, Q$ and $R$ respectively, then

A current carrying wire of length $L$ is suspended horizontally by a spring of force constant $K$ as shown. The system is in equilibrium. A magnetic field $B$ is switched on into the plane of paper suddenly. Which of the following statements is correct?

In a region of crossed fields as shown, the strength of electric field is $E$ and that of magnetic field is $B.$ Three positively charged particles with speeds $V_1, V_2$ and $V_3$ are projected and their paths are shown. From this it implies that

Two charges $q_1$ and $q_2$ having same magnitude of charge are moving parallel to each other and they enter into a region of uniform magnetic field as shown. If they have same mass and the time spent by them in the magnetic field are $t_1$ and $t_2$ respectively, then