A charged particle moves in a circular path of radius $r$ in a uniform magnetic field $B,$ perpendicular to the plane of motion. The same particle is observed to move in a circular path around an infinite line charge $\lambda$ (charge/unit length), moving with the same kinetic energy as before. The charge to mass ratio of the particle is proportional to:

1. $\lambda Br$ 2. $\dfrac{\lambda Br}{r}$

3. $\dfrac{\lambda}{Br}$ 4. $\dfrac{\lambda}{B^2r^2}$

Subtopic: Lorentz Force |

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Q29:

A charged particle of charge

q,

$q,$ mass

m

$m$ moves in a circular path under the action of a uniform magnetic field, whose flux through this path is

ϕ .

$\phi.$ The magnetic moment due to the particle's motion is:

1.	$\dfrac{q^2\phi}{2m}$	2.	$\dfrac{q^2\phi}{2\pi m}$
3.	$\dfrac{q^2\phi}{m}$	4.	$\dfrac{q^2\phi}{\pi m}$

Subtopic: Magnetic Moment |

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Q30:

A current-carrying wire is placed in a uniform magnetic field and the force on the wire is measured at different angular positions of the wire, as it is rotated in the

x - y

$x-y$ plane. Initially, the wire is along the

x

$x$ -axis. The magnitude of the magnetic force

(F)

$(F)$ is plotted as a function of the angle

(θ)

$(\theta)$ made by the current-carrying wire with the

x

$x$ -axis.

Which of the following is the possible magnetic field (in tesla)?
1.

2 \hat{j}

$2\hat j$
2.

2 \hat{k}

$2\hat k$
3.

2 \hat{i} + 2 \hat{k}

$2\hat i+2\hat k$
4.

2 \hat{j} + 2 \hat{k}

$2\hat j+2\hat k$

Subtopic: Magnetic Field due to various cases |

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Q31:

A long straight current-carrying wire is placed along the axis of a solenoid and it is found that the field within the solenoid at a distance of

\frac{r}{10}

$\dfrac r{10}$ from the wire is doubled when a current

I

$I$ passes through the wire and the solenoid,

r

$r$ being the radius of the solenoid. The number of turns per unit length of the solenoid are:

1.	$\dfrac{5}{\sqrt3r}$	2.	$\dfrac{5}{\sqrt3\pi r}$
3.	$\dfrac{5}{r}$	4.	$\dfrac{5}{\pi r}$

Subtopic: Magnetic Field due to various cases |

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Q32:

An ammeter having a resistance of

0.1 Ω

$0.1~ \Omega$ can measure a maximum current of

2 A

$2~\text{A}$ . To convert it into a voltmeter that can measure upto

50 V,

$50~\text{V},$ one must add:

1.	a resistance of $25~\Omega$ in series
2.	a resistance of $\dfrac1{25}~\Omega$ in series
3.	a resistance of $25~\Omega$ in parallel
4.	a resistance of $\dfrac1{25}~\Omega$ in parallel

Subtopic: Conversion to Ammeter & Voltmeter |

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Q33:

A charged particle (charge:

q

$q$ ) moves in a circular orbit in a uniform magnetic field, its orbit enclosing a magnetic flux

Φ .

$\Phi.$ The angular momentum of the particle is:

1.	$q\Phi$	2.	$\dfrac{q\Phi}{2\pi}$
3.	$\pi q\Phi$	4.	$\dfrac{q\Phi}{\pi}$

Subtopic: Lorentz Force |

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Q34:

A galvanometer

G

$G$ (having very small resistance), when connected with a resistance of

10 k Ω

$10~\text k\Omega$ in series, can function as a voltmeter measuring a maximum voltage of

20

$20$ V. The current required to give a full scale deflection on the galvanometer is:
1.

0.1

$0.1$ mA
2.

0.2

$0.2$ mA
3.

1

$1$ mA
4.

2

$2$ mA

Subtopic: Moving Coil Galvanometer |

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Q35:

A conducting wire is bent into the form of a square

A B C D,

$ABCD,$ and electrical connections are established in two different ways:

(I)	at two adjacent vertices $A,B$
(II)	at two points $A,C$ at the ends of a diagonal.

The same potential difference is established between the two connected ends. Current is, however, allowed to take only a single path from the positive to the negative terminal by disconnecting the other path. Let the magnetic field at the centre in these cases be

B_{I}, B_{II} .

$B_\text I,B_\text{II}.$ Then,

\frac{B_{I}}{B_{II}} =

$\frac{B_\text I}{B_\text{II}}=$

1.	$2$	2.	$\dfrac12$
3.	$\dfrac{1}{\sqrt2}$	4.	$1$

Subtopic: Magnetic Field due to various cases |

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Q36:

A charged particle of charge

q,

$q,$ mass

m

$m$ moves in a circular path in a uniform magnetic field

B .

$B.$ The current due to the motion of this particle has the average value:

1.	$\dfrac{q^2B}{2\pi m}$	2.	$\dfrac{qB^2}{m}$
3.	$\dfrac{2\pi m}{q^2B}$	4.	$\dfrac{qB}{m^2}$

Subtopic: Lorentz Force |

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Q37:

Two long parallel wires carrying currents

I_{1}

$I_1$ and

I_{2}

$I_2$ give a magnetic field of

3

$3$ G at a point exactly mid-way between the two wires. When one of the currents is reversed, the field becomes

5

$5$ G. The ratio of the large current to the smaller one is:

1.	$2$	2.	$\dfrac43$
3.	$\dfrac32$	4.	$4$

Subtopic: Magnetic Field due to various cases |

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1.	$\lambda Br$	2.	$\dfrac{\lambda Br}{r}$
3.	$\dfrac{\lambda}{Br}$	4.	$\dfrac{\lambda}{B^2r^2}$

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