A current-carrying loop of wire in the shape of a square of side $a$ lies in the $x\text-y$ plane. A uniform magnetic field $B$ acts in the plane. Then:

1. The force on the loop is $4iaB$ .

2. The torque on the loop is $ia^2B$ .

3. The force on the loop is $\sqrt {2} iaB$ .

4. The torque on the loop is $\sqrt{2}ia^2B$ .

Subtopic: Lorentz Force |

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Q6:

Two long parallel wires carry currents, equal to

i

$i$ each, in opposite directions. The distance between the wires is

d

$d$ . The net magnetic field, at a point which is at an equal distance

d

$d$ from each of the wires, is:

1.	$\dfrac{\mu_{0} i}{2 \pi d}$	2.	$\dfrac{2\mu_{0} i}{2 \pi d}$
3.	$\dfrac{\sqrt 3\mu_{0} i}{2 \pi d}$	4.	zero

Subtopic: Magnetic Field due to various cases |

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Q7:

When a particle of charge $q$ and mass $m$ is projected perpendicular to a magnetic field, it moves in a circle of radius $r.$ When the particle is projected upward with the same kinetic energy in a uniform gravitational field $(g)$ , it rises to a height $h$ . The magnetic field is:

1.	$\dfrac{m}{q r} \sqrt{\dfrac{g h}{2}}$	2.	$\dfrac{2m}{q r} \sqrt{\dfrac{g h}{2}}$
3.	$\dfrac{m}{2q r} \sqrt{\dfrac{g h}{2}}$	4.	none of the above.

Subtopic: Lorentz Force |

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Q8:

A long solenoid has a square cross-section of side

a

$a$ . It has turn-density n (number of turns per unit axial length). A current

i

$i$ is passed through this solenoid. The magnetic field at the centre of the solenoid is

B_{c}

$B_c$ . Then,

B_{c}

$B_c$ is proportional to:
(I)

a

$a$
(II)

\frac{1}{a}

$\dfrac{1} {a}$
(III)

n

$n$
(IV)

i

$i$
Choose the correct option from the given ones:
1. I, III, IV
2. II, III, IV
3. III, IV
4. IV Only

Subtopic: Magnetic Field due to various cases |

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Q9:

Two current carrying loops of wire are placed as shown in the figure, the inner loop

(P)

$(P)$ having a radius

(r)

$(r)$ which is much smaller than the radius

(R)

$(R)$ of the outer loop

(Q)

$(Q)$ . Both the loops are concentric, but the currents in one case are in the same sense while in the other, in the opposite sense.

In both cases, the torque on

P

$P$ due to

Q

$Q$ is zero. If

P

$P$ is slightly rotated about a diameter, then, it will return to its initial position in:

1.	case (I) but not in case (II).
2.	case (II) but not in case (I).
3.	both cases (I) and (II).
4.	neither of cases (I) and (II).

Subtopic: Magnetic Moment |

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Q10:

Two very long wires of length

L

$L$ are placed parallel to each other separated by a distance

r (r << L)

$r(r << L)$ . The wires carry equal currents

i

$i$ . The force between the two wires is nearly:

1.	$\dfrac{\mu_{0} i^{2} L}{2 \pi r}$	2.	$\dfrac{\mu_{0} i^{2} L}{4 \pi r}$
3.	$\dfrac{\mu_{0} i^{2} L}{2 r}$	4.	$\dfrac{\mu_{0} i^{2} L}{4 r}$

Subtopic: Force between Current Carrying Wires |

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Q11:

Identical cells are connected to identical square wire loops as shown in the two diagrams, and the magnetic fields are respectively

B_{1}

$B_1$ and

B_{2}

$B_2$ at the centres.

Then, we can conclude that:
1.

B_{1} > 0, B_{2} = 0

$B_1>0, B_2=0$
2.

B_{1} > B_{2} > 0

$B_1> B_2>0$
3.

B_{2} > B_{1} > 0

$B_2> B_1>0$
4.

B_{1} = 0, B_{2} = 0

$B_1=0, B_2=0$

Subtopic: Biot-Savart Law |

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Q12:

An

α

$\alpha$ -particle and a proton of the same kinetic energy move along circular paths of radii

r_{α}

$r_{\alpha}$ and

r_{p}

$r_p$ respectively, in the same magnetic field. The ratio

(r_{α} / r_{p})

$(r_{\alpha} / r_p)$ equals:

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

Subtopic: Lorentz Force |

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Q13:

A particle of mass

m

$m$ and the charge

q

$q$ is observed to move with a uniform velocity

v

$v$ in a region containing a uniform magnetic field

B,

$B,$ and a uniform gravitational field

g .

$g.$ The magnetic field

B

$B$ must satisfy:
1.

B = \frac{m g}{q v}

$B = \dfrac{mg}{qv}$

2.

B \leq \frac{m g}{q v}

$B \leq \dfrac{m g}{q v}$

3.

B \geq \frac{m g}{q v}

$B \geq \dfrac{m g}{q v}$

4.

B = \frac{q v}{m g}

$B = \dfrac{qv}{mg}$

Subtopic: Lorentz Force |

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Q14:

A straight long current-carrying wire carrying a current

i

$i$ is placed in a uniform magnetic field, and it is observed that the field vanishes at a point which is at a distance

r

$r$ from the wire. The force on the wire, per unit length, is:

1.	$\dfrac{\mu_{0} i^{2}}{2 \pi r}$	2.	$\dfrac{\mu_{0} i^{2}}{4 \pi r}$
3.	$\dfrac{\sqrt{2} \mu_{0} i^{2}}{2 \pi r}$	4.	$\dfrac{\mu_{0} r^{2}}{2 \pi r \sqrt{2}}$

Subtopic: Force between Current Carrying Wires |

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1.	The force on the loop is $4iaB$ .
2.	The torque on the loop is $ia^2B$ .
3.	The force on the loop is $\sqrt {2} iaB$ .
4.	The torque on the loop is $\sqrt{2}ia^2B$ .

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