$A$ uniform magnetic field exists in a region given by $\vec B = 3\hat i + 4\hat j + 2\hat k \, T$. $A$ conducting rod of length $5\,m$ is placed along the $y$-axis and is moved along the $x$-axis with a constant speed of $1\,m/s$. The $emf$ induced in the rod will be......$V$.

The wing span of an aeroplane is $20$ $m$. It is flying in a field where the vertical component of the Earth's magnetic field is $5 \times 10^{-5} \, T$,with a velocity of $360 \, km/h$. The potential difference produced between the wing tips will be ....... $V$.

The loops have lengths $L$ or $2L$. All loops enter a magnetic field $\vec{B}$ with the same velocity $v$. Which of the following is correct?

Figure $(i)$ shows a conducting loop being pulled out of a magnetic field with a speed $v$. Which of the four plots shown in figure $(ii)$ may represent the power delivered by the pulling agent as a function of the speed $v$?

In a region where the Earth's magnetic field is $3 \times 10^{-4} \, T$ with a dip angle $\theta = \tan^{-1}(4/3)$,a metal rod of length $0.25 \, m$ is placed in the North-South direction. If it is moved towards the East with a velocity of $10 \, cm/s$,calculate the induced $emf$ in $\mu V$.

$A$ square-shaped conducting wire loop of dimension $a$ moving parallel to the $X$-axis approaches a square region of size $b$ $(a < b)$,where a uniform magnetic field $B$ exists pointing into the plane of the paper (see figure). As the loop passes through this region,the plot correctly depicting its speed $v$ as a function of $x$ is