An electron is moving in a circular path under the influence of a transverse magnetic field of 3.57 × 10⁻² T. If the value of e/m is 1.76 × 10¹¹ C/kg, the frequency of revolution of the electron is:
A square loop ABCD carrying a current i is placed near and coplanar with a long straight conductor XY carrying a current I. The net force on the loop will be:
A long wire carrying a steady current is bent into a circular loop of one turn. The magnetic field at the centre of the loop is B. It is then bent into a circular coil of n turns. The magnetic field at the centre of this coil of n turns will be:
A long straight wire of radius a carries a steady current I. The current is uniformly distributed over its cross-section. The ratio of the magnetic fields B and B′ at radial distances a/2 and 2a respectively, from the axis of the wire, is:
An arrangement of three parallel straight wires placed perpendicular to the plane of paper carrying the same current 'I' along the same direction is shown in the figure. The magnitude of the force per unit length on the middle wire 'B' is given by:
A 250-turn rectangular coil of length 2.1 cm and width 1.25 cm carries a current of 85 A and is subjected to a magnetic field of strength 0.85 T. The work done for rotating the coil by 180° against the torque is:
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A metallic rod of mass per unit length 0.5 kg m⁻¹ is lying horizontally on a smooth inclined plane which makes an angle of 30° with the horizontal. The rod is not allowed to slide down by flowing a current through it when a magnetic field of induction 0.25 T is acting on it in the vertical direction. The current flowing in the rod to keep it stationary is:
Current sensitivity of a moving coil galvanometer is 5 div/mA and its voltage sensitivity (angular deflection per unit voltage applied) is 20 div/V. The resistance of the galvanometer is:
Ionized hydrogen atoms and α-particles with same momenta enter perpendicular to a constant magnetic field B. The ratio of the radii of their paths rₕ : r_α will be:
A straight conductor carrying current i splits into two parts as shown in the figure. The radius of the circular loop is R. The total magnetic field at the centre P of the loop is:
A cylindrical conductor of radius R is carrying a constant current. The plot of the magnitude of the magnetic field B with the distance d from the centre of the conductor is correctly represented by the figure:
A long solenoid of 50 cm length having 100 turns carries a current 2.5 A. The magnetic field at the centre of the solenoid is (μ₀ = 4π × 10⁻⁷ T m A⁻¹)
In the product F = q(v × B) = q(v_x î + v_y ĵ + v_z k̂) × (B_x î + B_y ĵ + B_z k̂), for q = 1 and v = 2î + 4ĵ + 6k̂ and F = 4î − 20ĵ + 12k̂, what will be the complete expression for B?
A thick current cable of radius R carries current 'I' uniformly distributed across its cross-section. The variation of magnetic field B(r) due to the cable with the distance 'r' from the axis of the cable is represented by:
An infinitely long straight conductor carries a current of 5 A as shown. An electron is moving with a speed of 10⁵ m/s parallel to the conductor. The perpendicular distance between the electron and the conductor is 20 cm at an instant. Calculate the magnitude of the force experienced by the electron at the instant.
A uniform conducting wire of length 12a and resistance 'R' is wound up as a current carrying coil in the shape of (i) an equilateral triangle of side 'a'. (ii) a square of side 'a'. The magnetic dipole moments of the coil in each case respectively are:
Given below are two statements. Statement I: Biot-Savart's law gives an expression for the magnetic field strength of an infinitesimal current element (Idl) of a current carrying conductor only. Statement II: Biot-Savart's law is analogous to Coulomb's inverse square law of charge q, with the former being related to the field produced by a scalar source, Idl, while the latter being produced by a vector source, q. In light of the above statements choose the most appropriate answer from the options given below:
A long solenoid of radius 1 mm has 100 turns per mm. If 1 A current flows in the solenoid, the magnetic field strength at the centre of the solenoid is:
From Ampère's circuital law for a long straight wire of circular cross-section carrying a steady current, the variation of magnetic field in the inside and outside region of the wire is:
A long straight wire of length 2 m and mass 250 g is suspended horizontally in a uniform horizontal magnetic field of 0.7 T. The amount of current flowing through the wire will be (g = 9.8 m s⁻²)
A wire carrying a current I along the positive x-axis has length L. It is kept in a magnetic field B = (2î + 3ĵ − 4k̂) T. The magnitude of the magnetic force acting on the wire is:
A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected in the region such that its velocity is pointed along the direction of fields, then the electron
A very long conducting wire is bent in a semi-circular shape from A to B as shown in figure. The magnetic field at point P for steady current configuration is given by:
A tightly wound 100 turns coil of radius 10 cm carries a current of 7 A. The magnitude of the magnetic field at the centre of the coil is (Take permeability of free space as 4π × 10⁻⁷ SI units):
A 2 A current is flowing through two different small circular copper coils having radii ratio 1 : 2. The ratio of their respective magnetic moments will be
An electron (mass 9 × 10⁻³¹ kg and charge 1.6 × 10⁻¹⁹ C) moving with speed c/100 (c = speed of light) is injected into a magnetic field B of magnitude 9 × 10⁻⁴ T perpendicular to its direction of motion. We wish to apply a uniform electric field E together with the magnetic field so that the electron does not deflect from its path. Then (speed of light c = 3 × 10⁸ m s⁻¹)
A model for quantized motion of an electron in a uniform magnetic field B states that the flux passing through the orbit of the electron is n(h/e), where n is an integer, h is Planck's constant and e is the magnitude of electron's charge. According to the model, the magnetic moment of an electron in its lowest energy state will be (m is the mass of the electron)
A 100-turn closely wound circular coil of radius 5 cm has a magnetic field of 3.14 × 10⁻³ T at its centre. The current flowing through the coil, and the magnitude of the magnetic moment of this coil are, respectively: (Take μ₀ = 4π × 10⁻⁷ T m/A)
A galvanometer of resistance 100 Ω gives full scale deflection for a current of 1 mA. It is converted into an ammeter of range 0 – 10 A. The shunt required is:
The figure shows a long straight solid wire of circular cross-section of radius 'a' carrying steady current I. The current I is uniformly distributed across its cross-section. The plot which correctly represents the variation of magnetic field (B) with distance (r) from the axis of the conductor is:
Two infinitely long parallel conducting wires $A$ and $B$ carry currents $I$ and $2I$ respectively in the same direction. Wire $A$ has uniform mass per unit length $\lambda$ and lies on an insulated floor. Wire $B$ is kept fixed at a height $h$ above the floor. The minimum magnitude of $h$ so that wire $A$ does not rise from the floor is: [$g$ = acceleration due to gravity, $\mu_0$ = permeability of free space]
A current $I_0$ flows through a metallic circular loop of radius $r$. The resistance of segment $ABC$ is half that of $ADC$. The magnitude of the magnetic field at the centre $O$ of the loop is:
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