$A$ charged particle is released from rest in a region of uniform electric and magnetic fields,which are parallel to each other. The locus of the particle will be

An electron (mass = $9.0 \times 10^{-31} \ kg$ and charge = $1.6 \times 10^{-19} \ C$) is moving in a circular orbit in a magnetic field of $1.0 \times 10^{-4} \ Wb/m^2$. Its period of revolution is:

$A$ particle having the same charge as an electron moves in a circular path of radius $0.5 \, cm$ under the influence of a magnetic field of $0.5 \, T$. If an electric field of $100 \, V/m$ makes it move in a straight path,then the mass of the particle is (given charge of electron $= 1.6 \times 10^{-19} \, C$):

$A$ charged particle moving along a straight line path enters a uniform magnetic field of $4 \ mT$ at right angles to the direction of the magnetic field. If the specific charge of the charged particle is $8 \times 10^7 \ C \ kg^{-1}$,the angular velocity of the particle in the magnetic field is

$A$ particle having a mass of $10^{-2} \, kg$ carries a charge of $5 \times 10^{-8} \, C$. The particle is given an initial horizontal velocity of $10^5 \, m/s$ in the presence of an electric field $\vec{E}$ and a magnetic field $\vec{B}$. To keep the particle moving in a horizontal direction,it is necessary that:
$(1)$ $\vec{B}$ should be perpendicular to the direction of velocity and $\vec{E}$ should be along the direction of velocity.
$(2)$ Both $\vec{B}$ and $\vec{E}$ should be along the direction of velocity.
$(3)$ Both $\vec{B}$ and $\vec{E}$ are mutually perpendicular and perpendicular to the direction of velocity.
$(4)$ $\vec{B}$ should be along the direction of velocity and $\vec{E}$ should be perpendicular to the direction of velocity.
Which one of the following pairs of statements is possible?

Two infinitely long straight wires $A$ and $B$, each carrying current $I$, are placed on the $x$ and $y$-axes, respectively. The current in wires $A$ and $B$ flows along $-\hat{i}$ and $\hat{j}$ directions, respectively. The force on a charged particle having charge $q$, moving from position $r = d(\hat{i} + \hat{j})$ with velocity $v = v\hat{i}$ is: