Toroid

Q. Use Biot-Savart law to derive the expression for the magnetic field on the axis of a current carrying circular loop of radius R.

Draw the magnetic field lines due to a circular wire carrying current I.

Q. Magnetc field due to a current carrying circular loop of radius $12\text{cm}$ at its centre is $0.5\times {10}^{-4}\text{T}$. Find the magnetic field due to this loop at a point on the axis at a distance $5.0\text{cm}$ from centre.

1. $3.9\times {10}^{-5}\text{T}$
2. $7.8\times {10}^{-5}\text{T}$
3. $11.7\times {10}^{-5}\text{T}$
4. None of these

Q.

Why is the symbol for magnetic field ‘B’?

Q.

The magnetic susceptibility of a paramagnetic material at -73 ${}^{\circ }$C is 0.0075 and its value at - 173 ${}^{\circ }$ C will be

1. 0.015

2. 0.0045

3. 0.0075

4. 0.0030

Q. Internal forces can change

1. the linear momentum but not the kinetic energy.
2. the kinetic energy but not the linear momentum.
3. linear momentum as well as kinetic energy.
4. neither the linear momentum nor the kinetic energy.

Q. A toroid has a core of inner radius $20\text{cm}$ and outer radius $22\text{cm}$ around which $4200$ turns of a wire are wound. If the current in the wire is $10\text{A}$, what is the magnetic field inside the core ?

1. $3\times {10}^{-2}\text{T}$
2. $1\times {10}^{-2}\text{T}$
3. $4\times {10}^{-2}\text{T}$
4. $2\times {10}^{-2}\text{T}$

Q. A toroid has $1000\text{turns}$. The inner and outer radii of its core are $15\text{cm}$ and $17\text{cm}$ respectively. The magnetic field in the centre of core for a current of $0.985\text{A}$ is $1.97\text{T}$. The value of relative permeability of core is.

Q.

In a step-up transformer, the relation between the number of turns in primary ${\mathrm{N}}_{\mathrm{P}}$ and the number of turns in secondary ${\mathrm{N}}_S$ coils is

1. ${\mathrm{N}}_S$ is greater than ${\mathrm{N}}_{\mathrm{P}}$

2. ${\mathrm{N}}_{\mathrm{P}}$ is greater than ${\mathrm{N}}_S$

3. ${\mathrm{N}}_S$ is equal to ${\mathrm{N}}_{\mathrm{P}}$

4. ${\mathrm{N}}_{\mathrm{P}}=2{\mathrm{N}}_{\mathrm{S}}$

Q.

A solenoid of $1000$ turns per metre has a core with a relative permeability of $500$. Insulated windings of the solenoid carry an electric current of $5A$. The magnetic flux density produced by the solenoid is: (Permeability of free space $=4\times {10}^{-7}H/m$)

1. $2\times {10}^{-3}\pi T$

2. $\pi /5T$

3. ${10}^{-4}\pi T$

4. $\pi T$

Q. A toroid has a core (non–ferromagnetic) of inner radius 25 cm and outer radius 26 cm, around which 3500 turns of a wire are wound. If the current in the wire is 11 A, what is the magnetic field outside the toroid, inside the core of the toroid and in the empty space surrounded by the toroid.

1. $0,3\times {10}^{-2}T,0$
2. $3\times {10}^{-2}T,0,0$
3. $0,0,3\times {10}^{-2}T$
4. $3\times {10}^{-2}T,0,3\times {10}^{-1}$

Q. Define self-inductance of a coil. Obtain the expression for the energy stored in an inductor L connected across a source of emf.

Q.

A series$L-R$ circuit is connected to a battery of $emf$$V$. If the circuit is switched on at$t=0$, then the time at which the energy stored in the inductor reaches$(1/n)$ times of its maximum value, is:

1. $\frac{L}{R}\ln \left[\frac{\sqrt{n}}{\sqrt{n}+1}\right]$

2. $\frac{L}{R}\ln \left[\frac{\sqrt{n}}{\sqrt{n}-1}\right]$

3. $\frac{L}{R}\ln \left[\frac{\sqrt{n}+1}{\sqrt{n}-1}\right]$

4. $\frac{L}{R}\ln \left[\frac{\sqrt{n}-1}{\sqrt{n}}\right]$

Q.

A coil having an area $2m^2$ is placed in a magnetic field which changes from $1\raisebox{1ex}{$wb$}\!\left/ \!\raisebox{-1ex}{$m^2$}\right.$ to $4\raisebox{1ex}{$wb$}\!\left/ \!\raisebox{-1ex}{$m^2$}\right.$ in an interval of $2sec$. The $e.m.f$ induced in the coil will be

1. $4V$

2. $3V$

3. $1.5V$

4. $2V$

Q. A loop of wire is placed in a magnetic field $\overrightarrow{B}=0.3\hat{j}\text{T}$. Find the flux through the loop, if the area vector is $\overrightarrow{A}=(2\hat{i}+5\hat{j}-3\hat{k}){\text{m}}^2$

1. $1\text{Wb}$
2. $1.5\text{Wb}$
3. $2\text{Wb}$
4. $2.5\text{Wb}$

Q.

Two coils have self-inductance $L_1=4mH$ and $L_2=1mH$ respectively. The currents in the two coils are increased at the same rate. At a certain instant of time, both coils are given the same power. If $i_1$and $i_2$ are the currents in the two coils, at that instant of time respectively, then the value of ($\frac{i_1}{i_2}$) is?

1. $0$

2. $1$

3. $\frac{1}{2}$

4. $\frac{1}{4}$

Q. A toroidal coil of rectangular crossection has an inner radius a, outer radius b, height h and total number of turns N. Current in the toroid is $i$, and say $r$ is distance of a point from the center of toroid.

1. Magnetic field at the point decreases with r for 0 < r < a
2. Magnetic field at the point increases with r for a < r < b
3. Magnetic field is zero for r > b
4. Self inductance of toroid is $\frac{{\mu }_0{N}^{2}h}{2\pi }ln\left(\frac{b}{a}\right)$

Q. The variation of the intensity of magnetisation $\left(I\right)$ with respect to the magnetising field $\left(H\right)$ in a diamagnetic substance is described by the graph.

1. $\text{OD}$
2. $\text{OC}$
3. $\text{OB}$
4. $\text{OA}$

Q. Magnetic susceptibility ${\chi }_m$ for the super conductor is–

1. ${\chi }_m=0$
2. ${\chi }_m=1$
3. ${\chi }_m=-1$
4. ${\chi }_m=2$

Q. A toroid having a square cross-section of side $5\text{cm}$ and inner radius of $15\text{cm}$, has $500$ turns and carries a current of $0.8\text{A}$. What is the magnetic field just inside the outer radius of the toroid ?

1. $2\times {10}^{-4}\text{T}$
2. $3\times {10}^{-2}\text{T}$
3. $4\times {10}^{-4}\text{T}$
4. $4\times {10}^{-2}\text{T}$

Q. A toroid has $1000\text{turns}$. The inner and outer radii of its core are $15\text{cm}$ and $17\text{cm}$ respectively. The magnetic field in the centre of core for a current of $0.985\text{A}$ is $1.97\text{T}$. The value of relative permeability of core is.

Q. 7. A magnetic flux of 500 microWb per turn, passing through a solenoid of 200 turns, is reversed in direction in 20 milli sec, the average emf induced in thesolenoid is(1) 5 V (2) 2 V (3) 20 V (4) 10V

Q. Why MnO2 is anti ferromagnetic

Q. A coil wrapped around a toroid has inner radius of $10.0\text{cm}$ and an outer radius $20.0\text{cm}$. If the wire wrapped makes $600\text{turns}$ and carries current of $10.0\text{A}$. Choose the correct alternatives.
$[B_{max}$ and $B_{min}$ are maximum and minimum magnetic fields inside the toroid$]$

1. $B_{max}=12\text{mT}$
2. $B_{max}=6\text{mT}$
3. $B_{min}=6\text{mT}$
4. $B_{min}=3\text{mT}$

Q. A square loop of side a and resistance R is moved in the region of uniform magnetic field B (loop remaining completely inside field ), with a velocity v through a distance x . The work done is

Q. A closely wound, solenoid $80\text{cm}$ long has $5$ layers of winding of $400$ turns each. The diameter of the solenoid is $1.8\text{cm}$. If the current carried is $8.0\text{A}$. Estimate the magnetic field Inside the solenoid

1. $2\pi \times {10}^{-3}\text{T}$
2. $16\pi \times {10}^{-3}\text{T}$
3. $8\pi \times {10}^{-3}\text{T}$
4. $4\pi \times {10}^{-3}\text{T}$

Q. A spring balance is attached to a plate of a parallel plate capacitor as shown in the figure.If sigma and -sigma are surface charge densities of plates and A is area of each plate, then reading of the spring balaance is

Q. The magnetic field insides a toroid of radius $r$ is $B$. If the radius of toroid is quadrupled and number of turns is increased by $8$ times keeping the current constant. Find the new magnetic field inside the core of toroid.

1. $B$
2. $\frac{B}{2}$
3. $2B$
4. $4B$

Q.

Two very long straight parallel wires 1 and 2 are separated by a small distance and carry the same current I. The current in wire 1 flows out of the page and that in wire 2 flows into the page. What is the direction of the magnetic field at point P due to the current in the wires? Point P is equidistant from the wires as shown in the figure below.

1. To the right.

2. To the left

3. Upward

4. Downward

Q. WHY ELECTRIC LINES OF FORCES ARE PERPENDICULAR TO THE SURFACE OF CONDUCTOR?

Q. A moving coil galvanometer has 48 turns and area of coil is $4\times {10}^{-2}{m}^2$. If the magnetic field is 0.2T then to increase the current sensitivity by 25% without changing area and B, the no.of turns should become

1. 20
2. 30
3. 40
4. 60