$A$ particle of charge $2 \ C$ is moving with a velocity of $(3 \hat{i} + 4 \hat{j}) \ ms^{-1}$ in the presence of magnetic and electric fields. If the magnetic field is $(\hat{i} + 2 \hat{j} + 3 \hat{k}) \ T$ and the electric field is $(-2 \hat{k}) \ NC^{-1}$, then the Lorentz force on the particle is: (in $N$)

$A$ particle of charge $q$ and velocity $v$ passes undeflected through a space with non-zero electric field $E$ and magnetic field $B$. The undeflected condition will hold if:

$A$ particle having charge $10^{-9} \text{ C}$ moving in the $x-y$ plane in fields of $0.4 \hat{i} \text{ N/C}$ and $4 \times 10^{-3} \hat{k} \text{ T}$ experiences a force of $(4 \hat{i} + 2 \hat{j}) \times 10^{-10} \text{ N}$. The velocity of the particle at that instant is . . . . . . $\text{m/s}$.

Give the definition of $1\, T$ (Tesla) magnetic field.

An electron enters an electric field with intensity $\vec{E} = 3\hat{i} + 6\hat{j} + 2\hat{k} \text{ V m}^{-1}$ and a magnetic field with induction $\vec{B} = 2\hat{i} + 3\hat{j} \text{ T}$ with a velocity $\vec{v} = 2\hat{i} + 3\hat{j} \text{ m s}^{-1}$. The magnitude of the force acting on the electron is (Given, $e = -1.6 \times 10^{-19} \text{ C}$)

In a certain region,static electric and magnetic fields exist. The magnetic field is given by $\vec B = B_0(\hat i + 2\hat j - 4\hat k)$. If a test charge moving with a velocity $\vec v = v_0(3\hat i - \hat j + 2\hat k)$ experiences no force in that region,then the electric field in the region,in $SI$ units,is