Solenoid

Q.

The earths magnetic field at the equator is approximately $0.4\times {10}^{-4}T$. What is the earths dipole moment?$R_e=6.4\times {10}^{6}m$.

Q. Why magnetic field in a infinte solenoid is half at its end

Q. The lines of force of the electric field due to two charges $q$ and $Q$ are sketched in the figure. State if

1. $q$ is negative and $|Q|<|q|$
2. $Q$ is positive and $|Q|>|q|$
3. $Q$ is negative and $|Q|>|q|$
4. $q$ is positive and $|Q|<|q|$

Q. The magnetic field at point $\text{P}$ due to the arrangement shown in figure is

1. $\frac{{\mu }_{0}I}{2\pi d}(\sqrt{2}-1)$
2. $\frac{{\mu }_{0}I}{4\pi d}(\sqrt{2}-1)$
3. $\frac{{\mu }_{0}I}{2\pi d}(1+\frac{1}{\sqrt{2}})$
4. $\frac{{\mu }_{0}I}{2\pi d}(1-\frac{1}{\sqrt{2}})$

Q. An equilateral triangle of side $a$ carries a current $i$, then the magnetic field at the vertex $\text{P}$ of triangle is

1. $\frac{{\mu }_{0}i}{2\sqrt{3}\pi a}\otimes$
2. $\frac{{\mu }_{0}i}{2\sqrt{3}\pi a}\odot$
3. $\frac{2\sqrt{3}{\mu }_{0}i}{\pi a}\odot$
4. zero

Q.

The dimensional formula for the magnetic moment of a magnet is.

Q. Find magnetic field at the point $P$.

1. $\frac{(\sqrt{2}\pi +2){\mu }_{0}I}{8\sqrt{2}\pi R}$
2. $\frac{3(\sqrt{2}\pi +1){\mu }_{0}I}{8\sqrt{2}\pi R}$
3. $\frac{(3\sqrt{2}\pi +2){\mu }_{0}I}{8\sqrt{2}\pi R}$
4. $\frac{(\sqrt{2}\pi +1){\mu }_{0}I}{4\sqrt{2}\pi R}$

Q. A $3.0cm$ wire carrying a current of $10A$ is a placed inside a solenoid perpendicular to its axis. The magnetic field inside the solenoid is given to be $0.27T$. What is magnetic force on the wire?

Q. The temperature coefficient of resistance of tungsten is 4.5 x 10^{-3} ^° C^{-1} and that of germanium is 5 x 10^{-2} ^° C^{-1}, A tungsten wire of resistance 100 Ω is connected in series with a germanium wire ofresistance R. The value of R for which the resistance of combination does not change with temperature is (1) 9Ω (2) 1111Ω (3) 0.9 Ω (4) 111.1Ω

Q. There are 50 turns of a wire in every $1cm$ length of a long solenoid. If a $4A$ current is flowing in the solenoid, the approximate value of magnetic field along its axis at an internal point and at one end will be respectively

1. $12.6\times {10}^{-3}\frac{Weber}{m^2},6.3\times {10}^{-3}\frac{Weber}{m^2}$
2. $12.6\times {10}^{-3}\frac{Weber}{m^2},25.1\times {10}^{-3}\frac{Weber}{m^2}$
3. $25.1\times {10}^{-3}\frac{Weber}{m^2},12.6\times {10}^{-3}\frac{Weber}{m^2}$
4. $25.1\times {10}^{-5}\frac{Weber}{m^2},6.3\times {10}^{-5}\frac{Weber}{m^2}$

Q. A long solenoid has 200 turns per cm and carries a current of 2.5 amps. The magnetic field at its centre is (${\mu }_0=4\pi \times {10}^{-7}weber/amp-m$)

1. 
2. 
3. 
4. 

Q.

The magnetic intensity H at the centre of a long solenoid carrying a current of 2.0 A, is found to be 1500 A $m^{-1}$. Find the number of turns per centimetre of the solenoid.

Q. A) Predict the direction of induced current in the situation described by the following figure


B) Predict the direction of induced current in the situation described by the following figure


C) Predict the direction of induced current in the situation described by the following figure


D) Predict the direction of induced current in the situation described by the following figure


E) Predict the direction of induced current in the situation described by the following figure



F) Predict the direction of induced current in the situation described by the following figure

Q. Two short magnets with their axes horizontal and perpendicular to the magnetic meridian are placed with their centres $40\text{cm}$ east and $50\text{cm}$ west of the magnetic needle. If the needle remains undeflected, the ratio of their magnetic moments $M_1:M_2$ is

1. $2:\sqrt{5}$
2. $64:125$
3. $16:25$
4. $4:5$

Q. The magnetic field at a distance $x$ on the axis of a circular coil of radius $R$ is $\frac{1}{8}$ th of that at the centre. The value of $x$ is

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

Q.

A copper wire having resistance 0.01 ohm in each metre is used to wind a 400-turn solenoid of radius 1.0 cm and length 20 cm. Find the emf of a battery which when connected across the solenoid will cause a magnetic field of 1$1.0\times {10}^{-2}T$ near the centre of the solenoid.

Q. The current as a function of time through a $4.6\text{H}$ inductor is shown in the following graph. The induced emf during the time interval $t=5\text{ms}$ to $6\text{ms}$ will be -

1. $20\text{kV}$
2. $23\text{kV}$
3. $26\text{kV}$
4. $29\text{kV}$

Q. Field inside a solenoid is

1. Directly proportional to current
2. Directly proportional to its length
3. Inversely proportional to total number of turns
4. Inversely proportional to current

Q. Find the equivalent inductance between $\text{A}$ and $\text{B}$ is-

1. $3.66\text{H}$
2. $9\text{H}$
3. $0.66\text{H}$
4. $1\text{H}$

Q.

The magnetic field B inside a long solenoid, carrying a current of 5.00 A, is $3.14\times {10}^{-2}T.$ Find the number of turns per unit length of the solenoid.

Q. A silver wire has diameter 0.4mm and resistivity 1.6 x10power-8.How much length of this where is required to make a 1 ohm coil.

Q. Two coaxial solenoids 1 and 2 of the same length are set so that one is inside the other. The number of turns per unit length are $n_1$ and $n_2$. The currents $i_1$ and $i_2$ are flowing in opposite directions. The magnetic field inside the inner coil is zero. This is possible when

1. $i_1\ne i_2$ and $n_1=n_2$
2. $i_1=i_2$ and $n_1\ne n_2$
3. $i_1\ne i_2$ and $n_1=n_2$
4. $i_1{n}_1=i_2{n}_2$

Q. A solenoid 60 cm long and of radius 4.0 cm has 3 layers of windingsof 300 turns each. A 2.0 cm long wire of mass 2.5 g lies inside thesolenoid (near its centre) normal to its axis; both the wire and theaxis of the solenoid are in the horizontal plane. The wire is connectedthrough two leads parallel to the axis of the solenoid to an externalbattery which supplies a current of 6.0 A in the wire. What value ofcurrent (with appropriate sense of circulation) in the windings ofthe solenoid can support the weight of the wire? g = 9.8 m s–2.

Q. In the figure shown, two long wires $w_1$ and $w_2$, each carrying current $I$ are placed parallel to each other and parallel to $z$- axis. The direction of current in $w_1$ and $w_2$ is perpendicularly outward and inward to the plane respectively. The $\overrightarrow{B}$ at point $\text{P}$ will be given as:

1. $\overrightarrow{B}=\frac{2{\mu }_{0}I}{5\pi a}\hat{i}+\frac{{\mu }_{0}I}{5\pi a}\hat{j}$
2. $\overrightarrow{B}=\frac{{\mu }_{0}I}{2\pi a}\hat{i}-\frac{{\mu }_{0}I}{5\pi a}\hat{j}$
3. $\overrightarrow{B}=\frac{2{\mu }_{0}I}{5\pi a}\hat{j}$
4. $\overrightarrow{B}=\frac{{\mu }_{0}I}{5\pi a}\hat{i}-\frac{{\mu }_{0}I}{5\pi a}\hat{j}$

Q. Calculate the magnetic field at a point located at a distance $\frac{\sqrt{3}}{2}a$ from midpoint of the straight wire of length $a$ carrying a current of $I$. The point lies on the perpendicular bisector of the wire.

1. $\frac{{\mu }_0}{4\pi }\frac{I}{a}$
2. $\frac{{\mu }_{0}I}{4\pi a}\frac{2}{\sqrt{3}}$
3. $\frac{{\mu }_{0}I}{2\pi a}\frac{2}{\sqrt{3}}$
4. None of these

Q. The current $i$ in a coil varies with time $t$ according to the graph shown below. Which of the following graphs, shows the induced emf $\left(E\right)$ in the coil with time?

1. 
2. 
3. 
4. 

Q. A wire loop formed by joining two semicircular wires of radii $R_1$ and $R_2$ carries a current as shown in the adjoining diagram. The current in the loop is $I$ and it is placed in a uniform magnetic field $B$, parallel to its plane. What will be the torque acting on the loop?

1. $\pi IB(R{{}_1}^2+R{{}_2}^2)$
2. 
   $\frac{\pi IB(R{{}_1}^2+R{{}_2}^2)}{2}$
3. $\pi IB(R{{}_2}^2-R{{}_1}^2)$
4. $\frac{\pi IB(R{{}_2}^2-R{{}_1}^2)}{2}$

Q.

A tightly-wound, long solenoid is kept with its axis parallel to a large metal sheet carrying a surface current. The surface current through a width dl of the sheet is Kdl and the number of turns per unit length of the solenoid is n. The magnetic field near the centre of the solenoid is found to be zero. (a) Find the current in the solenoid. (b) If the solenoid is rotated to make its axis perpendicular to the metal sheet, what would be the magnitude of the magnetic field near its centre ?

Q. A current $I$ is flowing through the sides of the rectangle as shown below. The magnetic field at the crossing point of the diagonal is

1. $\frac{4{\mu }_{0}I}{\pi a}$
2. $\frac{4{\mu }_{0}I}{\sqrt{3}\pi a}$
3. $\frac{{\mu }_{0}I}{\pi a}$
4. $\frac{{\mu }_{0}I}{3\pi a}$

Q. Magnetic field at point P at a distance d from vertex of infinite wire carrying current $i$ as shown in figure is

1. $\frac{{\mu }_0}{2\pi }\frac{i}{d}$
2. $\frac{{\mu }_{0}i}{4\pi d}(1-\sqrt{3})$
3. $\frac{{\mu }_0}{4\pi }\frac{i}{d}(2-\sqrt{3})$
4. $\frac{{\mu }_0}{\pi }\frac{i}{d}$