$A$ conducting square frame of side $a$ and a long straight wire carrying current $I$ are located in the same plane as shown in the figure. The frame moves to the right with a constant velocity $V$. The $emf$ induced in the frame will be proportional to

Two straight conducting rails form a right angle as shown below. $A$ conducting bar in contact with the rails starts at the vertex at time $t=0$ and moves with a constant velocity of $v=5 \ m \ s^{-1}$ along them. $A$ magnetic field with $B=0.1 \ T$ is directed out of the page. The absolute value of the emf induced in the circuit at time $t=4 \ s$ will be (in $V$)?

$A$ conducting rod with resistance $r$ per unit length is moving inside a vertical magnetic field $\overrightarrow B$ at speed $v$ on two horizontal parallel ideal conductor rails. The ends of the rails are connected to a resistor $R$. The separation between the rails is $d$. The rod maintains a tilted angle $\theta$ to the rails. Find the external force required to keep the rod moving.

Find the current in the wire for the configuration shown in the figure. Wire $PQ$ has negligible resistance. $\vec{B}$ is the magnetic field coming out of the paper. $\theta$ is a fixed angle made by $PQ$ as it travels smoothly over two conducting parallel wires separated by a distance $d$.

Derive the expression for the mechanical power required to move a conducting rod of length $l$ with a constant velocity $v$ in a uniform magnetic field $B$.

An aeroplane is travelling horizontally towards west with a speed of $540 \,km/h$. The wing span of the plane is $20 \,m$. If the horizontal component of the earth's magnetic field at the location is $2.5 \sqrt{3} \times 10^{-4} \,T$ and the dip angle is $30^{\circ}$,the potential difference developed between the ends of the wing is (in $\,V$)