Magnetic Field Due to a Circular Ring on the Axis

Q. An infinitely long straight conductor is bent into the shape as shown in the figure. It carries a current of i ampere and the radius of the circular loop is r metre. Then the magnetic induction at its centre will be

1. Infinite
2. 
3. 
4. Zero

Q. On what factors does the magnitude of induced EMF in a coil depends?

Q. A thread carrying a uniform charge $\lambda$ per unit length has the configuration shown in figures. Assuming a curvature radius R to be considerably less than the length of the thread, find the magnitude of the electric field strength at the point O.

1. $Zero,\frac{\sqrt{2k\lambda }}{R}$
2. Zero, zero
3. $\frac{\sqrt{2}k\lambda }{R},\frac{\sqrt{2}k\lambda }{R}$
4. $\frac{\sqrt{2}k\lambda }{R},zero$

Q.

Why inductor behaves as a short circuit?

Q. A metallic solid sphere is placed in a uniform electric field. The lines of force follow the path(s) shown in figure as

1. 1
2. 2
3. 4
4. 3

Q.

Two point charges $q_1=2\mu C$ and $q_2=1\mu C$ are placed at distances b = 1 cm and a = 2 cm from the origin of the y and x axes as shown in figure. The electric field vector at point P(a, b) will subtend an angle $\theta$ with the x-axis given by $tan\theta =K$. Find value of K.___

Q. An electron and a proton enter a region of uniform magnetic field in a direction perpendicular to the field with the same kinetic energy. They revolve in circular paths of radii $r_e$ and $r_p$ respectively. Then

1. $r_e=r_p$
2. $r_e<r_p$
3. $r_e>r_p$
4. $r_e$ may be less or greater than $r_p$

Q.

The quantities $x=\frac{1}{\sqrt{{\mu }_{\circ }{\epsilon }_{\circ }}},y=\frac{E}{B}$ and $z=\frac{L}{CR}$are defined where $C$-capacitance, $R$- Resistance, $L$ - length, $E$- Electric field, $B$ - magnetic field and ${\epsilon }_0,{\mu }_0$ - free space permittivity and permeability respectively. Then:

1. Only $y$ and $z$ have the same dimension

2. $x,y$ and $z$ have the same dimension

3. Only $x$ and $y$ have the same dimension

4. Only $x$ and $z$ have the same dimension

Q. An electron accelerated by a potential difference $V$ enters a uniform magnetic field of flux density $B$ at right angles to the field. It describes a circular path of radius $r$. If $V$ and $B$ are doubled, then the radius of the new circular path is

1. $\frac{r}{\sqrt{2}}$
2. $2\sqrt{2}r$
3. $2r$
4. $4r$

Q. A 2μ C charge moving around a circle with the frequency of 6.25x10^{12} Hz produces a magnetic field 6.28 tesla at the centre of the circle. The radius of the circle is A) 2.25m B)0.25m C)13.0m D)1.25m

Q. An electron is revolving around a proton, producing a magnetic field of $16{\text{Wb m}}^{-2}$ in a circular orbit of radius $1\mathring{\text{A}}.$ It's angular velocity will be

1. ${10}^{17}{\text{rad s}}^{-1}$
2. $\frac{1}{2\pi }{10}^{12}{\text{rad s}}^{-1}$
3. $2\pi \times {10}^{12}{\text{rad s}}^{-1}$
4. $4\pi \times {10}^{12}{\text{rad s}}^{-1}$

Q.

The figure shows a region of length$‘l’$ with a uniform magnetic field of $0.3T$ in it and a proton entering the region with velocity $4\times {10}^{5}m{s}^{-1}$ making an angle $60°$ with the field. If the proton completes $10revolution$ by the time it cross the region shown, $‘l’$ is close to (mass of proton =$1.67\times {10}^{–27}kg$, a charge of the proton = $1.6\times {10}^{–19}C$)

1. $0.11m$

2. $0.22m$

3. $0.44m$

4. $0.88m$

Q. A spherical conductor of radius $R$ carries charge $Q$ on its surface. The value of electric field just outside the surface of the conductor is $E$. If the radius of the counductor is doubled while keeping the charge same, what will be the value of new electric field just outside the surface of the conductor?

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

Q. A and B are concentric circular conductors with center O and carrying currents $I_1$ and $I_2$ as shown in fig. The ratio of their radii is 1: 2 and ratio of their flux densities at O is 1:3 The value of $\frac{I_1}{I_2}$ is

1. $\frac{1}{6}$
2. $\frac{1}{4}$
3. $\frac{1}{2}$
4. $\frac{1}{3}$

Q. PARAGRAPH
Consider an evacuated cylindrical chamber of height $h$ having rigid conducting plates at the ends and an insulating curved surface as shown in the figure. A number of spherical balls made of a light weight and soft material and coated with a conducting material are placed on the bottom plate. The balls have a radius $r<<h$. Now a high voltage source (HV) is connected across the conducting plates such that the bottom plate is at $+V_0$ and the top plate at $-V_0$. Due to their conducting surface, the balls will get charged, will become equipotential with the plate and are repelled by it. The balls will eventually collide with the top plate, where the coefficient of restitution can be taken to be zero due to the soft nature of the material of the balls. The electric field in the chamber can be considered to be that of a parallel plate capacitor. Assume that there are no collisions between the balls and the interaction between them is negligible. (Ignore gravity)

The average current in the steady state registered by the ammeter in the circuit will be

1. proportional to $V_0^2$
2. proportional to the potential $V_0$
3. zero
4. proportional to $V_0^{1/2}$

Q.

Find the magnetic induction of the field at the point O of a loop with current I, whose shape is illustrated in the figure.

1. $\frac{{\mu }_{0}I}{3\pi }(\frac{3\pi }{2a}+\frac{\sqrt{2}}{b})$

2. $\frac{{\mu }_{0}I}{2\pi }(\frac{3\pi }{4a}+\frac{\sqrt{2}}{2b})$

3. $\frac{{\mu }_{0}I}{2\pi }(\frac{2\pi }{3a}+\frac{\sqrt{2}}{b})$

4. $\frac{{\mu }_{0}I}{2\pi }(\frac{3\pi }{4a}+\frac{\sqrt{2}}{2b})$

Q.

Two concentric circular coils X and Y of radii 16 cm and 10 cm, respectively, lie in the same vertical plane containing the north to south direction. Coil X has 20 turns and carries a current of 16 A; coil Y has 25 turns and carries a current of 18 A. The sense of the current in X is anticlockwise, and clockwise in Y, for an observer looking at the coils facing west. Give the magnitude and direction of the net magnetic field due to the coils at their centre.

Q.

(a) Obtain an expression for the mutual inductance between a long straight wire and a square loop of side a as shown in Fig. 6.21.

(b) Now assume that the straight wire carries a current of 50 A and the loop is moved to the right with a constant velocity, v = 10 m/s.

Calculate the induced emf in the loop at the instant when x = 0.2 m.

Take a = 0.1 m and assume that the loop has a large resistance.

Q. A charged particle moving in a uniform magnetic field when losses $4\%$ of its kinetic energy, the radius of curvature of its circular path:

1. Decreases by $2\%$
2. Increases by $2\%$
3. Increases by $4\%$
4. Decreases by $4\%$

Q. A helium nucleus makes a full rotaion in a circle of radius $0.8\text{m}$ in two seconds. The value of the magnetic field $B$ at the centre of the circle will be

1. $\frac{{10}^{19}}{{\mu }_0}$
2. ${10}^{-19}{\mu }_0$
3. $2\times {10}^{-10}{\mu }_0$
4. $\frac{2\times {10}^{-10}}{{\mu }_0}$

Q. A circular current carrying coil has a radius R. The distance from the centre of the coil on the axis where the magnetic induction will be $\frac{1}{8}th$ to its value at the centre of the coil, is

1. $\frac{R}{\sqrt{3}}$
   
2. $R\sqrt{3}$
   
3. $2\sqrt{3}R$
   
4. $\frac{2}{\sqrt{3}}R$

Q. Two circular coils $X$ and $Y$, having equal number of turns and carrying equal currents in the same sense, subtend same solid angle at point $O$. If the smaller coil $X$ is midway between $O$ and $Y$ and if we represent the magnetic field due to bigger coil $Y$ at $O$ as $B_y$ and that due to smaller coil $X$ at $O$ as $B_x$, then

1. $\frac{B_y}{B_x}=1$
2. $\frac{B_y}{B_x}=\frac{1}{4}$
3. $\frac{B_y}{B_x}=2$
4. $\frac{B_y}{B_x}=\frac{1}{2}$

Q. A non-conducting disc, having uniformly distributed positive charge $Q$, is rotating about its axis with uniform angular velocity $\omega$. Choose the correct alternative(s).

1. The magnetic field at the centre of the disc is directed outward.
2. The magnetic field at the centre of the disc have magnitude $\frac{{\mu }_{0}Q\omega }{2\pi R}$
3. The magnetic field at the centre of the disc is directed inward.
4. The magnetic field at the centre of the disc have magnitude $\frac{{\mu }_{0}Q\omega }{4\pi R}$

Q.

Two circular coils of radii 5.0 cm and 10 cm carry equal currents of 2.0 A. The coils have 50 and 100 turns respectively and are placed in such a way that their planes as well as the centres coincide. Find the magnitude of the magnetic field B at the common centre of the coils if the currents in the coils are (a) in the same sense (b) in the opposite sense.

Q. (a) Using Biot-Savart's law, derive the expression for the magnetic field in the vector form at a point on the axis of a circular current loop.
(b) What does a toroid consist of ? Find out the expression for the magnetic field inside a toroid for N turns of the coil having the average radius r and carrying a current I. Show that the magnetic field in the open space inside and exterior to the toroid is zero.

Q. A straight wire of length $\left({\pi }^2\right)$ metre is carrying a current of 2A and the magnetic field due to it is measured at a point distant 1 cm from it. If the wire is to be bent into a circle and is to carry the same current as before, the ratio of the magnetic field at its centre to that obtained in the first case would be

1. 1 : 50
2. 50 : 1
3. 100 : 1
4. 1 : 100

Q.

Derive An Expression For Magnetic Field Strength At Any Point On The Axis Of A Circular Current Carrying Loop Using Biot-savart Law.

Q. A Rowland ring of mean radius 15 cm has 3500 turns of wire woundon a ferromagnetic core of relative permeability 800. What is themagnetic field B in the core for a magnetising current of 1.2 A?

Q. Two identical loops P and Q each of radius 5 cm are lying in perpendicular planes such that they have a common centre as shown in the figure. Find the magnitude and direction of the net magnetic field at the common centre of the two coils, if they carry currents equal to 3 A and 4 A respectively.

Q. At a certain place magnetic field vertically downwards. An electron approaches horizontally towards you and enters this magnetic field. It's trajectory, when seen from above will be a circle which is

1. Vertical clockwise
2. Vertical anticlockwise
3. Horizontal clockwise
4. Horizontal anticlockwise