An infinitely long straight wire carrying current I, one side ope… - Vidyadip

MCQ

An infinitely long straight wire carrying current $I,$ one side opened rectangular loop and a conductor $C$ with a sliding connector are located in the same plane, as shown in the figure. The connector has length $l$ and resistance $R$. It slides to the right with a velocity $V.$ The resistance of the conductor and the self inductance of the loop are negligible. The induced current in the loop, as a function of separation $r,$ between the connector and the straight wire is

A
$\frac{\mu_{0}}{\pi} \frac{ Iv l}{ Rr }$
✓
$\frac{\mu_{0}}{2 \pi} \frac{ Ivl }{ Rr }$
C
$\frac{2 \mu_{0}}{\pi} \frac{ Ivl }{ Rr }$
D
$\frac{\mu_{0}}{4 \pi} \frac{ Iv l}{ Rr }$

✓

Answer

Correct option: B.

$\frac{\mu_{0}}{2 \pi} \frac{ Ivl }{ Rr }$

b
$B =\frac{\mu_{0} i }{2 \pi r }$

$\phi=\frac{\mu_{0} i }{2 \pi r } \ell dr$

$\Rightarrow \frac{ d \phi}{ dt }=\frac{\mu_{0} i \ell}{2 \pi r } \cdot \frac{ dr }{ dt }$

$\Rightarrow e =\frac{\mu_{0}}{2 \pi} \cdot \frac{ iv \ell}{ r }$

$i =\frac{ e }{ R }=\frac{\mu_{0}}{2 \pi} \cdot \frac{ iv \ell}{ Rr }$

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

Explore more

More "M.C.Q (1 Marks)" from 6. Electromagnetic induction→6. Electromagnetic induction — all question types→Physics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

The equivalent capacitance between the points $A$ and $B$ in the given diagram is

The $r.m.s.$ value of potential difference $V$ shown in the figure is

$A$ concave mirror forms a real image three times larger than the object on a screen. Object and screen are moved until the image becomes twice the size of object. If the shift of object is $6\, cm$. The shift of the screen & focal length of mirror are

A bulb of 100 watt is hanging at a height of one meter above the centre of a circular table of diameter 4 m . If the intensity at a point on its rim is $I_0$, then the intensity at the centre of the table will be

The equivalent resistance between $P$ and $Q$ in the given figure, is ............... $\Omega$

The time period of rotation of the sun is 25 days and its radius is $7\times 10^8$ m. The Doppler shift for the light of wavelength 6000 Å emitted from the surface of the sun will be

For a common base circuit if $\frac{ I _{ C }}{ I _{ E }}=0.98$ then current gain for common emitter circuit will be

A potentiometer wire of length $10 \,m$ and resistance$20 \,\Omega$ is connected in series with a $25 \,V$ battery and an external resistance $30\, \Omega$. A cell of emf $E$ in secondary circuit is balanced by $250\, cm$ long potentiometer wire. The value of $E$ (in volt) is $\frac{x}{10}$. The value of $x$ is.......

A particle which has zero rest mass and non-zero energy and momentum must travel with a speed

An $N-P-N$ transistor in a common emitter mode is used as a simple voltage amplifier with a collector current of $4\ mA$ . The terminal of a $8\ V$ battery is connected to the collector through a load resistance $R_L$ and to the base through a resistance $R_B$ .The collector-emitter voltage $V_{CE} = 4\ V$ , base-emitter voltage $V_{BE} = 0.6\ V$ and base current amplification factor ${\beta _{d.c.}} = 100$ . Calculate the values of $R_L$ and $R_B$