MCQ
Suppose a long rectangular loop of width $w$ is moving along the $x$-direction with its left arm in a magnetic field perpendicular to the plane of the loop (see figure). The resistance of the loop is zero and it has an inductance $L$. At time, $t=0$, its left arm passes the origin, $O$. If for $t \geq 0$, the current in the loop is $I$ and the distance of its left arm from the origin is $x$, then $I$ versus $x$ graph will be
  • A


  • C

  • D

Answer

Correct option: B.

b
$(b)$ The circuit can be drawn as,

From the circuit,

$e-L \frac{d I}{d t}=0 \Rightarrow v B l-L \frac{d I}{d t}=0$

or $\quad v B l=L \frac{d I}{d t}$ or $\frac{d I}{d t}=\frac{v B l}{L}$ ..... $(i)$

As, $\quad x=v t$

$\Rightarrow \quad \frac{d x}{d t}=v$ ......$(ii)$

From Eqs. $(i)$ and $(ii)$, we get $\frac{d I}{d x}=\frac{B l}{L}=$ positive slope

Hence, graph shown in option $(b)$ is correct.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

The capacitor of an oscillatory circuit of negligible resistance is enclosed in a evacuated container. The frequency of the circuit is $150 \ kHZ$ and when the container is filled with a gas, the frequency changes by $100 \ HZ$. The dielectric constant of the gas.
Assertion : The capacity of a given conductor remains same even if charge is varied on it.
Reason : Capacitance depends upon nearly medium as well as size and shape of conductor.
A radioactive sample has half-life of $5$ years. Probability of decay in $10$ years will be  ........$\%$
Assertion : In the process of photoelectric emission, all the emitted photoelectrons have the same kinetic energy.
Reason : The photon transfers its whole energy to the electron of the atom in photoelectric effect.
In a double slit arrangement fringes are produced using light of wavelength $4800 Å$. One slit is covered by a thin plate of glass of refractive index $1.4$ and the other with another glass plate of same thickness but of refractive index $1.7$. By doing so the central bright shifts to original fifth bright fringe from centre. Thickness of glass plate is......$\mu m$
Calculate the charge on the second capacitor before and after switch in the circuit is closed
The power dissipated in the circuit shown in the figure is $30\, Watts$. The value of $R$ is ............. $\Omega$
The de-Broglie wavelength of a neutron at $27^oC$ is $\lambda$ What will be its wavelength at $927^oC$
The force on a hemisphere of radius $1\, cm$ if a parallel beam of monochromatic light of wavelength $500\, nm$. falls on it with an intensity of $0.5\, W/cm^2$, striking the curved surface in a direction which is perpendicular to the flat face of the hemisphere is (assume the collisions to be perfectly inelastic)
A mgnetic needle is kept in a non-uniform magnetic field. It experiences