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A small square loop of side ‘\( a \)’ and one turn is placed inside a larger square loop of side \( b \) and one turn \( (b \gg a) \). The two loops are coplanar with their centres coinciding. If a current \( I \) is passed in the square loop of side ‘\( b \)’, then the coefficient of mutual inductance between the two loops is:

There are two infinitely long straight current carrying conductors and they are held at right angles to each other so that their common ends meet at the origin as shown in the figure given below. The ratio of current in both conductors is \( 1:1 \). The magnetic field at point \( P \) is:

Two short magnetic dipoles \( m_1 \) and \( m_2 \) each having magnetic moment of \( 1 \, \text{A m}^2 \) are placed at point \( O \) and \( P \) respectively. The distance between \( OP \) is \( 1 \, \text{meter} \). The torque experienced by the magnetic dipole \( m_2 \) due to the presence of \( m_1 \) is ________ \( \times 10^{-7} \) \( \text{N m} \).

Two ions having same mass have charges in the ratio \( 1:2 \). They are projected normally in a uniform magnetic field with their speeds in the ratio \( 2:3 \). The ratio of the radii of their circular trajectories is:

A proton and an \( \alpha -\)particle, having kinetic energies \( K_{p} \) and \( K_{\alpha} \) respectively, enter into a magnetic field at right angles. The ratio of the radii of trajectory of proton to that of \( \alpha \)–particle is \( 2:1 \). The ratio of \( K_{p} : K_{\alpha} \) is:

If the maximum value of accelerating potential provided by a radio frequency oscillator is \( 12 \, \text{kV} \). The number of revolution made by a proton in a cyclotron to achieve one sixth of the speed of light is _____.
[ \( m_p = 1.67 \times 10^{-27} \, \text{kg} \), \( e = 1.6 \times 10^{-19} \, \text{C} \), Speed of light \( = 3 \times 10^{8} \, \text{m/s} \) ] .

In a uniform magnetic field, the magnetic needle has a magnetic moment \( 9.85\times 10^{-2} \, \text{A} / \text{m}^{2} \) and moment of inertia \( 5\times 10^{-6} \, \text{kg m}^{2} \). If it performs \( 10 \) complete oscillations in \( 5 \) seconds then the magnitude of the magnetic field is ________ \( \text{mT} \). [Take \( \pi^{2} \) as \( 9.85 \)]

A deuteron and an alpha particle having equal kinetic energy enter perpendicularly into a magnetic field. Let \( r_d \) and \( r_\alpha \) be their respective radii of circular path. The value of \( \dfrac{r_d}{r_\alpha} \) is

A hairpin like shape as shown in figure is made by bending a long current carrying wire. What is the magnitude of a magnetic field at point \( P \) which lies on the centre of the semicircle?

A coil having \( N \) turns is wound tightly in the form of a spiral with inner and outer radii ‘\( a \)’ and ‘\( b \)’ respectively. Find the magnetic field at centre, when a current \( I \) passes through coil:

Figure A and B show two long straight wires of circular cross-section (\( a \) and \( b \) with \( a < b \)), carrying current \( I \) which is uniformly distributed across the cross-section. The magnitude of magnetic field \( B \) varies with radius \( r \) and can be represented as:

Statement I: The ferromagnetic property depends on temperature. At high temperature ferromagnet becomes paramagnet.
Statement II: At high temperature, the domain wall area of a ferromagnetic substance increases.
In the light of the above statements, choose the most appropriate answer from the options given below

A loop of flexible wire of irregular shape carrying current is placed in an external magnetic field. Identify the effect of the field on the wire.

A current of \(\ 1.5 \, \text{A} \) is flowing through a triangle, of side \(\ 9 \, \text{cm} \) each. The magnetic field at the centroid of the triangle is: (Assume that the current is flowing in the clockwise direction.)

Two ions of masses \( 4 \, \text{amu} \) and \( 16 \, \text{amu} \) have charges \( +2e \) and \( +3e \) respectively. These ions pass through the region of constant perpendicular magnetic field. The kinetic energy of both ions is same. Then:

The fractional change in the magnetic field intensity at a distance \( r \) from centre on the axis of current carrying coil of radius\( a \) to the magnetic field intensity at the centre of the same coil is: (Take \( r \ll a \)).

Which of the following statements are correct?
\( (A) \) Electric monopoles do not exist whereas magnetic monopoles exist.
\( (B) \) Magnetic field lines due to solenoid at its ends and outside cannot be completely straight and confined.
\( (C) \) Magnetic field lines are completely confined within a toroid.
\( (D) \) Magnetic field lines inside a bar magnet are not parallel.
\( (E) \) \( \chi = -1 \) is the condition for a perfect diamagnetic material, where \( \chi \) is its magnetic susceptibility.
Choose the correct answer from the options given below.

Choose the correct option:

A charge \( Q \) is moving \( \vec{dl} \) distance in the magnetic field \( \vec{B} \). Find the value of work done by \( \vec{B} \).

A long solenoid with \( 1000 \) turns/m has a core material with relative permeability \( 500 \) and volume \( 10^{3} \, \text{cm}^{3} \). If the core material is replaced by another material having relative permeability of \( 750 \) with same volume maintaining same current of \( 0.75 \, \text{A} \) in the solenoid, the fractional change in the magnetic moment of the core would be approximately \( \left( \frac{x}{499} \right) \). Find the value of \( x \).

A uniform conducting wire of length \( 24a \), and resistance \( R \) is wound up as a current carrying coil in the shape of an equilateral triangle of side \( a \) and then in the form of a square of side \( a \). The coil is connected to a voltage source \( V_0 \). The ratio of magnetic moment of the coils of equilateral triangle to that for square is \( 1 : \sqrt{y} \) where \( y \) is __________.

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

A coil in the shape of an equilateral triangle of side \( 10 \, \text{cm} \) lies in a vertical plane between the pole pieces of permanent magnet producing a horizontal magnetic field \( 20 \, \text{mT} \). The torque acting on the coil when a current of \( 0.2 \, \text{A} \) is passed through it and its plane becomes parallel to the magnetic field will be \( \sqrt{x}\times 10^{-5} \, \text{Nm} \). The value of \( x \) is ____________.

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JEE Main 2021 31st August Morning Shift

A coil having \( N \) turns is wound tightly in the form of a spiral with inner and outer radii ‘\( a \)’ and ‘\( b \)’ respectively. Find the magnetic field at centre, when a current \( I \) passes through coil: