In the given branch $AB$ of a circuit,a current $I = (10t + 5) \, A$ is flowing,where $t$ is time in seconds. At $t = 0$,the potential difference between points $A$ and $B$ $(V_A - V_B)$ is.....$V$.

The horizontal component of the earth's magnetic field at a place is $3 \times 10^{-4} \ T$ and the dip is $\tan^{-1}(4/3)$. $A$ thin metal rod of length $0.25 \ m$ placed in the north-south position is moved at a constant speed of $10 \ cm/s$ towards the east. Find the $e.m.f.$ induced in the rod across its ends in $\mu V$.

$A$ circular wheel with $10$ spokes, with its plane vertical along East-West, is rotating about its natural axis with a uniform speed of $100$ revolutions per minute in the Earth's magnetic field. The radius of the wheel is $0.3 \, m$. If the $EMF$ induced between the centre of the wheel and the rim is $3 \pi \mu V$, what is the angle of dip at that place? (Vertical component of the Earth's magnetic field $B_{V} = 15 \mu T$)

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?

$A$ 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

$A$ conducting rod $AC$ of length $4l$ is rotated about a point $O$ in a uniform magnetic field $\vec{B}$ directed into the paper. $AO = l$ and $OC = 3l$. Then which of the following is incorrect?