$A$ particle of mass $m$ and charge $q$ is in an electric and magnetic field given by $\vec E = 2\hat i + 3\hat j$ and $\vec B = 4\hat j + 6\hat k$. The charged particle is shifted from the origin $(0, 0, 0)$ to the point $P(1, 1, 0)$ along a straight path. The magnitude of the total work done is: (in $q$)

In the product $\overrightarrow{F} = q(\vec{v} \times \overrightarrow{B})$ where $\overrightarrow{B} = B \hat{i} + B \hat{j} + B_{0} \hat{k}$. Given $q = 1$,$\vec{v} = 2 \hat{i} + 4 \hat{j} + 6 \hat{k}$,and $\overrightarrow{F} = 4 \hat{i} - 20 \hat{j} + 12 \hat{k}$,what is the complete expression for $\overrightarrow{B}$?

An electric charge $+q$ moves with velocity $\overrightarrow{V} = 3\hat{i} + 4\hat{j} + \hat{k}$ in an electromagnetic field given by $\overrightarrow{E} = 3\hat{i} + \hat{j} + 2\hat{k}$ and $\overrightarrow{B} = \hat{i} + \hat{j} - 3\hat{k}$. The $y$-component of the force experienced by $+q$ is: (in $q$)

$A$ 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 $N$)

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, $e = -1.6 \times 10^{-19} \text{ C}$)

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