$A$ straight line conductor of length $0.4 \ m$ is moved with a speed of $7.0 \ ms^{-1}$ perpendicular to a magnetic field of intensity $0.8 \ Wb \ m^{-2}$. The induced e.m.f. across the conductor is (in $V$)

Consider the situation shown in the figure. The wire $AB$ is sliding on the fixed rails with a constant velocity. If the wire $AB$ is replaced by a semicircular wire,the magnitude of the induced current will

Refer to the figure. The arm $PQ$ of the rectangular conductor is moved from $x=0$ outwards. The uniform magnetic field is perpendicular to the plane and extends from $x=0$ to $x=b$ and is zero for $x>b$. Only the arm $PQ$ possesses substantial resistance $r$. Consider the situation when the arm $PQ$ is pulled outwards from $x=0$ to $x=2b$ and is then moved back to $x=0$ with constant speed $v$. Obtain expressions for the flux,the induced emf,the force necessary to pull the arm,and the power dissipated as Joule heat. Sketch the variation of these quantities with distance.

$A$ rod of length $60 \ cm$ rotates with a uniform angular velocity $20 \ rad \ s^{-1}$ about its perpendicular bisector in a uniform magnetic field of $0.5 \ T$. The direction of the magnetic field is parallel to the axis of rotation. The potential difference between the two ends of the rod is . . . . . . $V$.

Consider a metal ball of radius $r$ moving at a constant velocity $v$ in a uniform magnetic field of induction $\vec{B}$. Assuming that the direction of velocity forms an angle $\alpha$ with the direction of $\vec{B}$,the maximum potential difference between points on the ball is

Consider the situation shown in the figure. The wire $PQ$ has a negligible resistance and is made to slide on the three rails with a constant speed of $5 \, cm/s$. Find the current in the $10 \, \Omega$ resistor when the switch $S$ is connected to the middle rail. (Given: $B = 1.0 \, T$) (in $mA$)