For a circular coil of radius R and N turns carrying current I, the magnitude of the magnetic field at a point on its axis at a distance x from its centre is given by, $B=\frac{{\mu }_{0}I{R}^{2}N}{2{\left(x^2+R^2\right)}^{{\displaystyle \frac{3}{2}}}}$

The magnetic field at the centre of the coil is:

$$\begin{gathered} \left(1\right) \frac{{\mu }_{0}I N}{R} \\ \left(2\right) \frac{2{\mu }_{0}I N}{R} \\ \left(3\right) 0 \\ \left(4\right) \frac{{\mu }_{0}I N}{2R} \end{gathered}$$

A closely wound solenoid of 2000 turns and area of cross-section as $1.6\times {10}^{-4} m^2$ , carrying a current of 4.0 A, is suspended through its center allowing it to turn in a horizontal plane. The magnetic moment associated with the solenoid is:

$$\begin{gathered} \left(1\right) 0.18 A{m}^2 \\ \left(2\right) 3.24 A{m}^2 \\ \left(3\right) 1.28 A{m}^2 \\ \left(4\right) 0.38 A{m}^2 \end{gathered}$$

A monoenergetic electron beam with an electron speed of 5.20 x 10⁶ m/s is subject to a magnetic field of 1.30 x 10^-4 T normal to the beam velocity. What is the radius of the circle traced by the beam, given e/m for electron equals 1.76 x 10¹¹ C kg^-1?

An electron gun with its collector at a potential of 100 V fires out electrons in a spherical bulb containing hydrogen gas at low pressure $\left(~{10}^{-2} mm of Hg\right).$ A magnetic field of $2.83\times {10}^{-4} T$ curves the path of the electrons in a circular orbit of radius 12.0 cm. (The path can be viewed because the gas ions in the path focus the beam by attracting electrons, and emitting light by electron capture; this method is known as the 'fine beam tube' method. Specific charge ratio (e/m) is:

$$\begin{gathered} \left(1\right) 1.21\times {10}^{11} C k{g}^{-1} \\ \left(2\right) 1.73\times {10}^{11} C k{g}^{-1} \\ \left(3\right) 2.53\times {10}^{11} C k{g}^{-1} \\ \left(4\right) 3.02\times {10}^{11} C k{g}^{-1} \end{gathered}$$

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, the magnetic field inside the core of the toroid is:

$$\begin{gathered} \left(1\right) 3\times {10}^{-2} T \\ \left(2\right) 0 \\ \left(3\right) 2\times {10}^{-3} T \\ \left(4\right) 1\times {10}^{-2} T \end{gathered}$$

An electron emitted by a heated cathode and accelerated through a potential difference of 2.0 kV, enters a region with a uniform magnetic field of 0.15 T. if the field is transverse to its initial velocity, the radius of the circular path is:

A circular coil of wire consisting of 100 turns, each of radius 8.0 cm carries a current of 0.40 A. What is the magnitude of the magnetic field B at the centre of the coil?

$$\begin{gathered} \left(1\right) 3.14\times {10}^{-4} T \\ \left(2\right) 2.12\times {10}^{-4} T \\ \left(3\right) 1.41\times {10}^{-4} T \\ \left(4\right) 2.01\times {10}^{-4} T \end{gathered}$$

Two moving coil meters, M₁ and M₂ have the following particulars: 

R₁ = 10 Ω, N₁ = 30, A₁ = 3.6 x 10^-3 m² and B₁ = 0.25 T

R₂ = 14 Ω, N₂ = 42, A₂ = 1.8 x 10^-3 m² and B₂ = 0.50 T

A square coil of side 10 cm consists of 20 turns and carries a current of 12 A. The coil is suspended vertically and the normal to the plane of the coil makes an angle of 30º with the direction of a uniform horizontal magnetic field of magnitude 0.80 T. What is the magnitude of torque experienced by the coil?

 The wires which connect the battery of an automobile to its starting motor carry a current of 300 A (for a short time). What is the force per unit length between the wires if they are 70 cm long and 1.5 cm apart?

Closely wound solenoid 80 cm long has 5 layers of windings of 400 turns each. The diameter of the solenoid is 1.8 cm. If the current carried is 8.0 A, the magnitude of B inside the solenoid near its centre is:

$$\begin{gathered} \left(1\right) 3.7\times {10}^{-2} T \\ \left(2\right) 3.1\times {10}^{-2} T \\ \left(3\right) 2.5\times {10}^{-2} T \\ \left(4\right) 1.44\times {10}^{-2} T \end{gathered}$$

Two long and parallel straight wires A and B carrying currents of 8.0 A and 5.0 A in the same direction are separated by a distance of 4.0 cm. the force on a 10 cm section of wire A is:

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

$$\begin{gathered} \left(1\right) 8.1\times {10}^{-2} N \\ \left(2\right) 9.8\times {10}^{-2} N \\ \left(3\right) 7.6\times {10}^{-2} N \\ \left(4\right) 6.8\times {10}^{-2} N \end{gathered}$$

What is the magnitude of magnetic force per unit length on a wire carrying a current of 8 A and making an angle of ${30}^0$ with the direction of a uniform magnetic field of 0.15 T?

A horizontal overhead power line carries a current of 90 A in the east to west direction. What is the magnitude and direction of the magnetic field due to the current 1.5 m below the line?

$$\begin{gathered} \left(1\right) 1.2\times {10}^{-5} T towards north \\ \left(2\right) 2.1\times {10}^{-5} T towards south \\ \left(3\right) 1.2\times {10}^{-5} T towards south \\ \left(4\right) 2.1\times {10}^{-5} T towards north \end{gathered}$$

A long straight wire in the horizontal plane carries a current of 50 A in the north to south direction. The magnitude and direction of the magnetic field at a point 2.5 m east of the wire is:

$$\begin{gathered} \left(1\right) 4\times {10}^{-6} T vertically upward \\ \left(2\right) 4\times {10}^{-6} T vertically downward \\ \left(3\right) 3\times {10}^{-6} T vertically upward \\ \left(4\right) 3\times {10}^{-6} T vertically downward \end{gathered}$$

A long straight wire carries a current of 35 A. The magnitude of the magnetic field at a point 20 cm from the wire is:

$$\begin{gathered} \left(1\right) 3.5\times {10}^{-6} T \\ \left(2\right) 3.5\times {10}^{-5} T \\ \left(3\right) 4.5\times {10}^{-6} T \\ \left(4\right) 4.5\times {10}^{-5} T \end{gathered}$$

A uniform magnetic field of 1.5 T exists in a cylindrical region of a radius of 10.0 cm, its direction parallel to its axis along east to west. A wire carrying a current of 7.0 A in the north to south direction passes through this region. What is the magnitude and direction of the force on the wire if the wire intersects the axis?

A circular coil of 20 turns and a radius of 10 cm is placed in a uniform magnetic field of 0.10 T normal to the plane of the coil. If the current in the coil is 5.0 A, what is the total torque on the coil?

A galvanometer coil has a resistance of 15 Ω and the metre shows full-scale deflection for a current of 4 mA. How will you convert the metre into an ammeter of range 0 to 6 A?

A galvanometer coil has a resistance of 12 $\Omega$ and the metre shows full-scale deflection for a current of 3 mA. How will you convert the metre into a voltmeter of range 0 to 18 V?

A solenoid 60 cm long and of radius 4.0 cm has 3 layers of windings of 300 turns each. A 2.0 cm long wire of mass 2.5 g lies inside the solenoid (near its centre) normal to its axis; both the wire and the axis of the solenoid are in the horizontal plane. The wire is connected through two leads parallel to the axis of the solenoid to an external battery which supplies a current of 6.0 A in the wire. What value of current (with an appropriate sense of circulation) in the windings of the solenoid can support the weight of the wire? $\left(g=9.8 m s^{-2}\right)$

A closely wound solenoid of 800 turns and area of cross-section $2.5\times {10}^{-4} m^2$ carries a current of 3.0 A. If the solenoid acts like a bar magnet. What is its associated magnetic moment?

$$\begin{gathered} \left(1\right) 0.6 J T^{-1} \\ \left(2\right) 0.7 J T^{-1} \\ \left(3\right) 0.3 J T^{-1} \\ \left(4\right) 0.8 J T^{-1} \end{gathered}$$

A monoenergetic (18 keV) electron beam initially in the horizontal direction is subjected to a horizontal magnetic field of 0.04 G normal to the initial direction. The up or down deflection of the beam over a distance of 30 cm is:  $\left(m_e=9.11\times {10}^{-31} kg\right).$

A magnetic dipole is under the influence of two magnetic fields. The angle between the field directions is $60°$, and one of the fields has a magnitude of $1.2\times {10}^{-2} T.$ If the dipole comes to stable equilibrium at an angle of $15°$ with this field, what is the magnitude of the other field?        $\left[Given: \sin 15°=0.26\right]$

$\begin{array}{rcl}& & 1. 7.29\times {10}^{-3} T\\ & & 2. 4.39\times {10}^{-3} T\\ & & 3. 6.18\times {10}^{-3} T\\ & & 4. 5.37\times {10}^{-3} T\end{array}$

A galvanometer of resistance 100 $\mathrm{\Omega }$ gives full-scale deflection at 10 mA current. What should be the value of the shunt so that it can measure a current of 100 mA?

A galvanometer coil has a resistance of 90 $\mathrm{\Omega }$ and a full-scale deflection current of 10 mA. A 910 $\mathrm{\Omega }$ resistance is connected in series with the galvanometer to make a voltmeter. If the least count of the voltmeter is 0.1 V, the number of divisions on the scale is:

A galvanometer with an internal resistance of 100$\Omega$ will show a full-scale deflection with a current of 10 mA. Which of the following circuits would turn this galvanometer into an ammeter which will read 10 A at full scale?

A direct current is passing through a wire. It is bent to form a coil of one turn. Now it is further bent to form coil of two turns but of smaller radius. The ratio of the magnetic induction at the centre of this coil and at the centre of the coil of one turn is:

In a region of space, magnetic field is parallel to the positive y-axis and the charged particle is moving along the positive x-axis (as shown in the figure). The directions of Lorentz force for an electron (negative charge) and proton (positive charge) are respectively: