A uniform but time varying magnetic field $B\left(t\right)$ exists in a.circular region of radius $a$ it is directed into the plane of the paper as shown. The magnitude of the induced electric field at point $P$ at a distance $r$ from the centre of the circular region.

Assertion: A resistance $R$ is connected between the two ends of the parallel smooth conducting rails. A conducting rod lies on these fixed horizontal rails and a uniform constant magnetic field $B$ exists perpendicular to the plane of the rails as shown in the figure. If the rod is given a velocity $v$ and released as shown in the figure, it will stop after some time. The total work done by the magnetic field is negative.

Reason: In this case, the resultant magnetic force on the free charges is opposite to the velocity of the free charges.

The galvanometer deflection. when key $K_1$ is closed but $K_2$ is open equals ${\theta }_0$ (see figure). On closing $K_2$ also and adjusting $R_2$ to $5 \mathrm{\Omega }$, the deflection in galvanometer becomes $\frac{{\theta }_0}{5}$.

The resistance of the galvanometer is given by (neglect the internal resistance of battery) :

A particle a mass of ${10}^{-2} \mathrm{kg}$ carries a charge of $5\times {10}^{-8}\mathrm{C}$. The particle is given an initial horizontal velocity of ${10}^5{ \mathrm{ms}}_{}^{-1}$ in the presence of electric field $\overrightarrow{E}$ and magnetic field $\overrightarrow{\mathrm{B}}$. To keep the particle moving in a horizontal direction, it is necessary that

(i) $\overrightarrow{B}$ should be perpendicular, to the direction of velocity and $\overrightarrow{E}$ should be along the direction of velocity.

(ii) Both $\overrightarrow{B}$ and $\overrightarrow{E}$ should be along the direction of velocity.

(iii) Both $\overrightarrow{B}$ and $\overrightarrow{E}$ are mutually perpendicular and perpendicular to the direction of velocity.

(iv) $\overrightarrow{B}$ should be along the direction of velocity and $\overrightarrow{E}$ should be perpendicular to the direction of velocity.

Which one of the following pairs of statements is possible?

A current carrying loop in the from of a right angle isosceles triangle $ABC$ is placed in a. uniform magnetic field acting along $AB$ if the magnetic force on the arm $BC$  is $\overrightarrow{F}$ the force on the arm $AC$ is