There exists a uniform magnetic field of magnitude $1\, T$ and a uniform electric field of magnitude $1\, V/m$ along the positive $y-$ axis. $A$ charged particle of mass $1\, kg$ and charge $1\, C$ has an initial velocity of $1\, m/s$ along the $x-$ axis and is at the origin at $t = 0$. Find the coordinates of the particle at time $t = \pi$ seconds.

$A$ conductor lies parallel to the $Z$-axis between $-1.5 \le Z < 1.5 \text{ m}$,carrying a constant current of $10.0 \text{ A}$ in the $-\hat{a}_z$ direction. For the given magnetic field $\vec{B} = 3.0 \times 10^{-4} e^{-0.2x} \hat{a}_y \text{ T}$,find the power required to move the conductor at a constant speed from $x = 0$ to $x = 2.0 \text{ m}$ in a time interval of $5 \times 10^{-3} \text{ s}$. Assume the motion is parallel to the $X$-axis. ........... $\text{W}$

$A$ thin,straight conductor lies along the axis of a hollow conductor of radius $R$. The two carry equal currents in the same direction. The magnetic field $B$ is plotted against the distance $r$ from the axis. Which of the following best represents the resulting curve?

$A$ $100$ turn closely wound circular coil of radius $10\; cm$ carries a current of $3.2\; A$.
$(a)$ What is the field at the centre of the coil?
$(b)$ What is the magnetic moment of this coil?
The coil is placed in a vertical plane and is free to rotate about a horizontal axis which coincides with its diameter. $A$ uniform magnetic field of $2\; T$ in the horizontal direction exists such that initially the axis of the coil is in the direction of the field. The coil rotates through an angle of $90^{\circ}$ under the influence of the magnetic field.
$(c)$ What are the magnitudes of the torques on the coil in the initial and final position?
$(d)$ What is the angular speed acquired by the coil when it has rotated by $90^{\circ}$? The moment of inertia of the coil is $0.1\; kg\; m^{2}$.

The temperature at which the thermo-electric power of a thermocouple becomes zero is called:

Which of the following statements is correct?