Tag: force on current carrying conductor

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Multiple choice force and torque on a current carrying rectangular loop in a uniform magnetic field torque on current carrying loop force on current carrying conductor magnetic effects of current and magnetism physics
The potential energy of a bar magnet of magnetic moment $M$ placed in a magnetic field of induction $B$. The position of stable equilibrium of the magnet is at the angular position given by $\theta$ equal to:
[where $\theta$ is the angle between B and M]

  1. ${0}^{o}$

  2. ${90}^{o}$

  3. ${45}^{o}$

  4. ${180}^{o}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Potential energy U = -M * B = -MB cos(theta). Stable equilibrium occurs at the minimum potential energy, which is when cos(theta) = 1, meaning theta = 0 degrees.

Multiple choice force and torque on a current carrying rectangular loop in a uniform magnetic field torque on current carrying loop force on current carrying conductor magnetic effects of current and magnetism physics

A circular coil of 25 turns and radius 12 cm is placed in a uniform magnetic field of 0.5 T normal to the plane of the coil. If the current in the coil is 6 A then total torque acting on the coil is

  1. zero

  2. 3.4 N m

  3. 3.8 N m

  4. 4.4 N m
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The torque acting on the coil $\tau$=|$\bar m$ X $\bar B$ | =$ mB\sin\Theta$
Here the circular coil is placed normal to the direction of magnetic field then the angle between the. direction of magnetic moment ($\bar m$) and magnetic field ($\bar B$) is zero, then
$\tau$ = $mBsin\Theta$ = $mBsin 0$ = 0                $\tau = 0$

Multiple choice force and torque on a current carrying rectangular loop in a uniform magnetic field torque on current carrying loop force on current carrying conductor magnetic effects of current and magnetism physics

The magnitude of torque experienced by a square coil of side 12 cm which consists of 25 turns and carries a current 10 A suspended vertically and the normal to the plane of coil makes an angle of 30 with the direction of a uniform horizontal magnetic field of magnitude 0.9 T is:

  1. 1.6 Nm

  2. 1.2 Nm

  3. 1.4 Nm

  4. 1.8 Nm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Here,
$N=25,\\ I=10A, \\B= 0.9T,\\\theta=30^0$

$A=a^2=12 \times 10^{-2} \times 12 \times 10^{-2} =144 \times 10^{-4}m^2$

       $\tau$= $NIA\sin\theta$

$\therefore \tau = 25 \times 10\times 144 \times 10^{-4} \times 0.9 \times \sin30^0 = 1.6Nm$  

Multiple choice force and torque on a current carrying rectangular loop in a uniform magnetic field torque on current carrying loop force on current carrying conductor magnetic effects of current and magnetism physics

A circular coil of 70 turns and radius 5 cm carrying a current of 8 A is suspended vertically in a uniform horizontal magnetic field of magnitude 1.5 T. The field lines make an angle of 30 with the normal of the coil then the magnitude of the counter torque that must be applied to prevent the coil from turning is :

  1. 33 N m

  2. 3 N m

  3. 3.3 x $10^{2}$N m

  4. 3.3 x $10^{-4}$N m
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Number of turns on the circular coil, $n = 70$

Radius of the coil, $r = 5.0 cm = 0.05\ m$

Area of the coil , $A= \pi r^2=3.14\times(0.05)^2= $

Current flowing in the coil, $I = 8.0\ A$

Magnetic field strength, $B = 1.5\ T$

Angle between the field lines and normal with the coil surface,

$θ = 30^o$

The coil experiences a torque in the magnetic field. Hence, it turns. The counter torque applied to prevent the coil from turning is given by the relation,

$\tau = n IBA sinθ$ … (i)

$\tau= 70 × 8 × 1.5 × 0.00785× sin30^o$

$\tau = 3.3\ N m$


Multiple choice force and torque on a current carrying rectangular loop in a uniform magnetic field torque on current carrying loop force on current carrying conductor magnetic effects of current and magnetism physics

A dipole of magnetic moment $\vec{m}=30\hat{j}$A $m^2$ is placed along the y-axis in a uniform magnetic field $\bar{B}=(2\hat{i}+5\hat{j})$T. The torque acting on it is?

  1. $-40\hat{k}$N m

  2. $-50\hat{k}$N m

  3. $-60\hat{k}$N m

  4. $-70\hat{k}$N m
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given that,

Magnetic moment of a dipole, $\vec m=30\hat j\ Am^2$
Magnetic field, $\vec B= (2\hat i+ 5\hat j)\ T$

Torque acting on the dipole , $\vec{\tau}= \vec m \times \vec B$

$\implies  \vec{\tau}= 30\hat j \times( 2\hat i +5\hat j)= -60 \hat k \ Nm $

Multiple choice force and torque on a current carrying rectangular loop in a uniform magnetic field torque on current carrying loop force on current carrying conductor magnetic effects of current and magnetism physics

A circular coil of $100$ turns, radius $10$cm carries a current of $5$A. It is suspended vertically in a uniform horizontal magnetic field of $0.5$T and the field lines make an angle of $60^0$ with the plane of the coil. The magnitude of the torque that must be applied on it to prevent it from turning is going to be

  1. $2.93$ N m

  2. $3.43$ N m

  3. $3.93$ N m

  4. $4.93$ N m
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given that,


Number of turns, $N=100$
Radius of coil, $r=10\ cm=0.1 \ m$
Current in the coil, $i=5\ A$
Magnetic moment of the coil, $M= Ni(\pi r^2)$
Magnetic field, $B=0.5\ T$
$\theta=90^o-60^o=30^o$

Torque that must be applied to the coil, $\tau = Ni(\pi r^2) \times B \times sin\ \theta=100\times 5\times (3.14\times 0.1^2)\times0.5\times sin 30^o=3.93\ Nm$

So, correct option is $(C)$

Multiple choice force and torque on a current carrying rectangular loop in a uniform magnetic field torque on current carrying loop force on current carrying conductor magnetic effects of current and magnetism physics

The torque and magnetic potential energy of a magnetic dipole in most stable position in a uniform magnetic field $(\bar{B})$ having magnetic moment $(\bar{m})$ will be

  1. $-mB, zero$

  2. $mB, zero$

  3. $zero, mB$

  4. $zero, -mB$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Torque, $\bar{T} = \bar{m} \times \bar{B} = mB sin \theta$
and magnetic potential energy $U _m = \bar{m}. \bar{B} = mB cos \theta$ at $\theta = 0^0$ the dipole will be in most stable position
$T = mB sin\theta = mB sin 0^0 = 0$
and $U _m = -mB cos\theta = -mB cos 0^0 = -mB$

Multiple choice force and torque on a current carrying rectangular loop in a uniform magnetic field torque on current carrying loop force on current carrying conductor magnetic effects of current and magnetism physics

The final torque on a coil having magnetic moment 25 A $m^2$ in a 5 T uniform external magnetic field, if the coil rotates through an angle of 60 under the influence of the magnetic field is:

  1. 216.5 Nm

  2. 108.25 Nm

  3. 102.5 Nm

  4. 58.1 Nm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Here, 
$m=25 A m^2 ; \\ \theta  = 60^0 ;\\ B = 5T$


$|\vec {\tau} = |\vec m \times \vec B |=mB\sin\Theta$

$\therefore  = 25 \times 5\times  \sin60^0$ or

 $\tau= 125 \times \dfrac{\sqrt3}{2} = 108.25 Nm$

Multiple choice force and torque on a current carrying rectangular loop in a uniform magnetic field torque on current carrying loop force on current carrying conductor magnetic effects of current and magnetism physics

The magnetic moment of a short bar magnet placed with its magnetic axis at $30^0$ to an external field of $900$G and experiences a torque of $0.02$N m is going to be

  1. $0.35 A m^2$

  2. $0.44 A m^2$

  3. $2.45 A m^2$

  4. $1.5 A m^2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Here, $B = 900 Gauss = 900 \times 10^{-4}T. = 9 \times 10^{-2}T$
$T = 0.02 N m and \theta = 30^0$
$\therefore T = mB sin \theta$
$\Rightarrow 0.02 = m \times 9 \times 10^{-2} \times sin 30^0$
$m = \dfrac{0.02 \times 2 }{9 \times 10^{-2}}= 0.44 A m^2$.

Multiple choice force and torque on a current carrying rectangular loop in a uniform magnetic field torque on current carrying loop force on current carrying conductor magnetic effects of current and magnetism physics

If a solenoid is having magnetic moment of $0.65 JT^{-1}$ is free to turn about the vertical direction and has a uniform horizontal magnetic field of $0.25$T applied. What is the magnitude of the torque on the solenoid when its axis makes an angle of $30^0$ with the direction of applied field is?

  1. $0.075$N m

  2. $0.080$ N m

  3. $0.081$ N m

  4. $0.091$ N m
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Given that, $M=0.65 JT^{-1}$ , $B=0.25\ T$ and $\theta= 30^o$

$\therefore$ Torque on the solenoid $, \tau =MB\sin \theta =0.65\times 0.25\times \sin 30^o$
$=0.65\times 0.25\times \dfrac{1}{2}=0.08125=0.081\ Nm$

So, option $(C)$ is correct.