$A$ copper rod $AB$ of length $L$,pivoted at one end $A$,rotates at a constant angular velocity $\omega$,at right angles to a uniform magnetic field of induction $B$. The e.m.f. developed between the midpoint $C$ of the rod and end $B$ is

At a place,the value of the horizontal component of the Earth's magnetic field $H$ is $3 \times 10^{-5} \, Wb/m^2$. $A$ metallic rod $AB$ of length $2 \, m$,placed in the east-west direction with end $A$ towards the east,falls vertically downward with a constant velocity of $50 \, m/s$. Which end of the rod becomes positively charged,and what is the value of the induced potential difference between the two ends?

The magnetic field in a region is given by $\overrightarrow{ B }= B _{0}\left(\frac{ x }{ a }\right) \,\hat{ k }$. $A$ square loop of side $d$ is placed with its edges along the $x$ and $y$ axes. The loop is moved with a constant velocity $\overrightarrow{ v }= v _{0} \hat{ i }$. The emf induced in the loop is:

Two parallel long straight conductors lie on a smooth surface. Two other parallel conductors rest on them at right angles so as to form a square of side $a$ initially. $A$ uniform magnetic field $B$ exists at right angles to the plane containing the conductors. They all start moving outwards with a constant velocity $v$. If $r$ is the resistance per unit length of the wire,the current in the circuit will be

$A$ small rectangular loop of wire in the plane of the paper is moved with uniform speed across a limited region of uniform magnetic field perpendicular to the plane of the paper as shown below. Which graph would best represent the variation of the electric current $I$ in the wire with time $t$?

$A$ $1 \ m$ long metal rod $AB$ completes the circuit as shown in the figure. The area of the circuit is perpendicular to the magnetic field of $0.10 \ T$. If the resistance of the total circuit is $2 \ \Omega$, then the force needed to move the rod towards the right with a constant speed $(v)$ of $1.5 \ m/s$ is . . . . . . $N$.