Q: A magnetic dipole in a constant magnetic field has ;

\$U= - \vec{\mu}. \vec{B}= \mu B cos\theta\$----------1\$\tau = \mu B sin\theta\$--------------2From 1 and 2, we can say that magnetic field has zero potential energy when the torque is maximum. Hence the answer and option C is correct

Q: Relative permittivity and permeability of a material are \$\epsilon_{\mathrm{r}}\$ and \$\mu_{\mathrm{r}}\$, respectively. Which of the following values of these quantifies are allowed for a diamagnetic material?

For a diamagnetic material, \$\mu_r\$ and \$\epsilon_r\$ should have following bounds \$0 1\$

Q: The B-H curve for a ferromagnet is shown in the figure. The ferromagnet is placed inside a ling solenoid with \$1000\$ turns/cm.. The current that should be passed in the solenoid to demagnetise the ferromagnet completely is:

\$N=1000 turns/cm \$\$H= \dfrac{NI}{l}\$\$100 \dfrac{A}{M} = \dfrac{1000 \times I}{10^{-2}}\$\$100 A = 10^5 \times I \$\$10^{-3}A=I\$\$I=1mA\$

Q: A tin rectangular magnet suspended freely has a period of oscillation equal to \$T\$. Now it is broken into equal halves (each having half of the original length) and one piece is mode to oscillate freely in the same field. If its period of oscillation is \$T'\$, the ratio \$\dfrac{T'}{T}\$ is :

\$m=\$ mass of rectangular magnet \$M=\$ Magnetic moment Moment of inertia, \$I_1\propto l^2 m\$Time period, T \$\propto \dfrac{\sqrt I}{\sqrt M}\$Therefore, time period \$T\propto l \times \sqrt{\dfrac{m}{M}}\$when magnet is cut then mass and magnetic moment becomes half.Hence, time period becomes halfOption B is answer.

Q: A planar loops of wire rotates in a uniform magnetic field. Initially, at \$t = 0\$, the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of \$10 s\$ about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at :

Time period, \$T = 10 s\$Ref. image IAxis of rotation \$\rightarrow \$ y-axis.\$\vec{B} = B(-\hat{k})\$ref. image IIat some time t, area vector makes angle '\$\theta\$' with \$\vec{B}\$.flux, \$\phi = \vec{B}. \vec{A}\$\$= BA \cos \theta\$emf, \$\varepsilon= \left|\dfrac{-d \phi}{dt} \right| = \left(BA \sin \theta \dfrac{d \theta}{dt}\right)\$\$= BA \omega \sin \theta\$When \$\theta = \dfrac{\pi}{2} , \varepsilon = \varepsilon_{max}\$So, \$\theta = n \pi + \dfrac{\pi}{2} \$ n = integes When \$\theta = 0, \varepsilon = \varepsilon_{min} = 0\$So, \$\theta = n \pi\$, n = integesfor \$\varepsilon = \varepsilon_{max}, \theta = \omega t = n \pi + \dfrac{\pi}{2}\$\$\Rightarrow t = \dfrac{n \pi}{\omega} + \dfrac{\pi}{2 \omega} = \dfrac{n \pi}{\left(\dfrac{2 \pi}{T} \right)} + \dfrac{\pi}{2 \times \left(\dfrac{2 \pi}{T} \right)}\$\$t = \left(\dfrac{n \pi}{\dfrac{2 \pi}{T}} \right) + \dfrac{\pi}{2 \left(\dfrac{2 \pi}{T} \right)}\$\$= \dfrac{n T}{2} + \dfrac{T}{4} = \dfrac{n \times 10}{2} + \dfrac{10}{4}\$\$= 5n + 2.5\$\$= 2.5 s, 5 + 2.5 , 5 \times 2 + 2.5 ...\$\$= 2.5 s, 7.5 s, 12.5 s....\$for \$\varepsilon = \varepsilon_{min}, \theta = \omega t = n \pi\$\$\Rightarrow t = \dfrac{n \pi}{\omega} = \dfrac{n \pi}{\left(\dfrac{2 \pi}{T} \right)} = \dfrac{n T}{2}\$\$\Rightarrow t = \dfrac{n \times 10}{2} = 5n\$\$= 0 s, 5s, 10s, ...\$So, possible option is option (C).

Question 1

A magnetic dipole in a constant magnetic field has ;

Accepted Answer

$U= - \vec{\mu}. \vec{B}= \mu B cos\theta$----------1$\tau = \mu B sin\theta$--------------2From 1 and 2, we can say that magnetic field has zero potential energy when the torque is maximum. Hence the answer and option C is correct

Question 2

Relative permittivity and permeability of a material are $ϵ_{r}$ and $μ_{r}$ , respectively. Which of the following values of these quantifies are allowed for a diamagnetic material?

Accepted Answer

For a diamagnetic material, $\mu_r$ and $\epsilon_r$ should have following bounds $0<\mu_r <1$ and for any material $\epsilon_r >1$

Question 3

The B-H curve for a ferromagnet is shown in the figure. The ferromagnet is placed inside a ling solenoid with $1000$ turns/cm.. The current that should be passed in the solenoid to demagnetise the ferromagnet completely is:

Accepted Answer

$N=1000 turns/cm $$H= \dfrac{NI}{l}$$100 \dfrac{A}{M} = \dfrac{1000 \times I}{10^{-2}}$$100 A = 10^5 \times I $$10^{-3}A=I$$I=1mA$

Question 4

A tin rectangular magnet suspended freely has a period of oscillation equal to $T$. Now it is broken into equal halves (each having half of the original length) and one piece is mode to oscillate freely in the same field. If its period of oscillation is $T'$, the ratio $\dfrac{T'}{T}$ is :

Accepted Answer

$m=$ mass of rectangular magnet $M=$ Magnetic moment Moment of inertia, $I_1\propto l^2 m$Time period, T $\propto \dfrac{\sqrt I}{\sqrt M}$Therefore, time period $T\propto l \times \sqrt{\dfrac{m}{M}}$when magnet is cut then mass and magnetic moment becomes half.Hence, time period becomes halfOption B is answer.

Question 5

Curie temperature is the temperature above which

Accepted Answer

Curie temperature is the temperature at which certain materials lose their permanent magnetic properties, to be replaced by induced magnetism.Permanent magnetism is caused by the alignment of magnetic moments and induced magnetism is created when disordered magnetic moments are forced to align in an applied magnetic field.  Higher temperatures make magnets weaker, as spontaneous magnetism only occurs below the Curie temperature.

Question 6

An example of a perfect diamagnet is a superconductor. This implies that when a superconductor is put in a magnetic field of intensity $B$, the magnetic field $B_S$ inside the superconductor will be such that :

Accepted Answer

A diamagnet has a tendency to repel the magnetic field lines passing through it.For a perfect diamagnet or a semiconductor, the field lines wont enter the superconductor at all Hence, the magnetic field inside the superconductor will be 0

Question 7

Three identical bars A, B and C are made of different magnetic materials. When kept in a uniform magnetic field, the field lines around them look as given in the figure . Make the correspondence of these bars with their material being diamagnetic (D), ferromagnetic (F) and paramagnetic (P) .

Accepted Answer

Magnet  A  is  allowing  all  the  field  lines  passing  through  it , therefore  it  is  ferromagnetic. Magnet  B  is  repelling  the  field  lines  therefore  it  is  diamagnet.Magnet  C  is  attracting  the  field  lines  therefore  it  is  paramagnet.

Question 8

Needles $N_{1}, N_{2}$ and $N_{3}$ are made of a ferromagnetic, a paramagnetic and a diamagnetic substance respectively. A magnet when brought close to them will

Accepted Answer

Ferromagnetic substances are strongly attracted by a magnet while, paramagnetic and diamaganetic substances are weakly attracted and repelled respectively.

Question 9

A planar loops of wire rotates in a uniform magnetic field. Initially, at $t = 0$, the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of $10 s$ about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at :

Accepted Answer

Time period, $T = 10 s$Ref. image IAxis of rotation $\rightarrow $ y-axis.$\vec{B} = B(-\hat{k})$ref. image IIat some time t, area vector makes angle '$\theta$' with $\vec{B}$.flux, $\phi = \vec{B}. \vec{A}$$= BA \cos \theta$emf, $\varepsilon= \left|\dfrac{-d \phi}{dt} \right| = \left(BA \sin \theta \dfrac{d \theta}{dt}\right)$$= BA \omega \sin \theta$When $\theta = \dfrac{\pi}{2} , \varepsilon = \varepsilon_{max}$So, $\theta = n \pi + \dfrac{\pi}{2} $   n = integes When $\theta = 0, \varepsilon = \varepsilon_{min} = 0$So, $\theta = n \pi$, n = integesfor $\varepsilon  = \varepsilon_{max}, \theta = \omega t = n \pi + \dfrac{\pi}{2}$$\Rightarrow t = \dfrac{n \pi}{\omega} + \dfrac{\pi}{2 \omega} = \dfrac{n \pi}{\left(\dfrac{2 \pi}{T} \right)} + \dfrac{\pi}{2 \times \left(\dfrac{2 \pi}{T} \right)}$$t = \left(\dfrac{n \pi}{\dfrac{2 \pi}{T}} \right) + \dfrac{\pi}{2 \left(\dfrac{2 \pi}{T} \right)}$$= \dfrac{n T}{2} + \dfrac{T}{4} = \dfrac{n \times 10}{2} + \dfrac{10}{4}$$= 5n + 2.5$$= 2.5 s, 5 + 2.5 , 5 \times 2 + 2.5 ...$$= 2.5 s, 7.5 s, 12.5 s....$for $\varepsilon = \varepsilon_{min}, \theta = \omega t = n \pi$$\Rightarrow t = \dfrac{n \pi}{\omega} = \dfrac{n \pi}{\left(\dfrac{2 \pi}{T} \right)} = \dfrac{n T}{2}$$\Rightarrow  t = \dfrac{n \times 10}{2} = 5n$$= 0 s, 5s, 10s, ...$So, possible option is option (C).

Question 10

The figure gives experimentally measured B vs. H variation in a ferromagnetic material. The retentivity, co-ercivity and saturation, respectively, of the material are :

Accepted Answer

The retentivity measures the induced magnetic field at which applied field is zero.So, Retentivity $= OA = 1.0T$Co-ercivity is the resistance of a ferromagnetic material to become demagnetized $= OC = 50 A/m$.$\therefore $ Co-ercivity $= 50 A/m$At saturation magnetization; graph becomes horizontal So, saturation magnetization $= M_s = 1.5 T$option (D) is correct.

Magnetism And Matter

Physics
7000 Views

A magnetic dipole in a constant magnetic field has ;

Relative permittivity and permeability of a material are $ϵ_{r}$ and $μ_{r}$ , respectively. Which of the following values of these quantifies are allowed for a diamagnetic material?

The B-H curve for a ferromagnet is shown in the figure. The ferromagnet is placed inside a ling solenoid with $1000$ turns/cm.. The current that should be passed in the solenoid to demagnetise the ferromagnet completely is:

A tin rectangular magnet suspended freely has a period of oscillation equal to $T$ . Now it is broken into equal halves (each having half of the original length) and one piece is mode to oscillate freely in the same field. If its period of oscillation is $T^{'}$ , the ratio $\frac{T ^{'}}{T}$ is :

Curie temperature is the temperature above which

An example of a perfect diamagnet is a superconductor. This implies that when a superconductor is put in a magnetic field of intensity $B$ , the magnetic field $B_{S}$ inside the superconductor will be such that :

Three identical bars A, B and C are made of different magnetic materials. When kept in a uniform magnetic field, the field lines around them look as given in the figure . Make the correspondence of these bars with their material being diamagnetic (D), ferromagnetic (F) and paramagnetic (P) .

Needles $N_{1}, N_{2}$ and $N_{3}$ are made of a ferromagnetic, a paramagnetic and a diamagnetic substance respectively. A magnet when brought close to them will

A planar loops of wire rotates in a uniform magnetic field. Initially, at $t = 0$ , the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of $10 s$ about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at :

The figure gives experimentally measured B vs. H variation in a ferromagnetic material. The retentivity, co-ercivity and saturation, respectively, of the material are :

Magnetism And Matter

Physics 7000 Views

A magnetic dipole in a constant magnetic field has ;

Relative permittivity and permeability of a material are ϵr​ and μr​, respectively. Which of the following values of these quantifies are allowed for a diamagnetic material?

The B-H curve for a ferromagnet is shown in the figure. The ferromagnet is placed inside a ling solenoid with 1000 turns/cm.. The current that should be passed in the solenoid to demagnetise the ferromagnet completely is:

A tin rectangular magnet suspended freely has a period of oscillation equal to T. Now it is broken into equal halves (each having half of the original length) and one piece is mode to oscillate freely in the same field. If its period of oscillation is T′, the ratio TT′​ is :

Curie temperature is the temperature above which

An example of a perfect diamagnet is a superconductor. This implies that when a superconductor is put in a magnetic field of intensity B, the magnetic field BS​ inside the superconductor will be such that :

Three identical bars A, B and C are made of different magnetic materials. When kept in a uniform magnetic field, the field lines around them look as given in the figure . Make the correspondence of these bars with their material being diamagnetic (D), ferromagnetic (F) and paramagnetic (P) .

Needles N1​,N2​ and N3​ are made of a ferromagnetic, a paramagnetic and a diamagnetic substance respectively. A magnet when brought close to them will

A planar loops of wire rotates in a uniform magnetic field. Initially, at t=0, the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of 10s about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at :

The figure gives experimentally measured B vs. H variation in a ferromagnetic material. The retentivity, co-ercivity and saturation, respectively, of the material are :

Physics
7000 Views

Relative permittivity and permeability of a material are $ϵ_{r}$ and $μ_{r}$ , respectively. Which of the following values of these quantifies are allowed for a diamagnetic material?

The B-H curve for a ferromagnet is shown in the figure. The ferromagnet is placed inside a ling solenoid with $1000$ turns/cm.. The current that should be passed in the solenoid to demagnetise the ferromagnet completely is:

A tin rectangular magnet suspended freely has a period of oscillation equal to $T$ . Now it is broken into equal halves (each having half of the original length) and one piece is mode to oscillate freely in the same field. If its period of oscillation is $T^{'}$ , the ratio $\frac{T ^{'}}{T}$ is :

An example of a perfect diamagnet is a superconductor. This implies that when a superconductor is put in a magnetic field of intensity $B$ , the magnetic field $B_{S}$ inside the superconductor will be such that :

Needles $N_{1}, N_{2}$ and $N_{3}$ are made of a ferromagnetic, a paramagnetic and a diamagnetic substance respectively. A magnet when brought close to them will

A planar loops of wire rotates in a uniform magnetic field. Initially, at $t = 0$ , the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of $10 s$ about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at :