Which one of the following current densities, can generate the magnetic vector potential
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Electromagnetic Theory
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A metal has free-electron density n = 1029 m-3. Which of the following wavelengths will excite plasma oscillations?
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The electric field of a plane electromagnetic wave is If and are cartesian unit vectors, the wave vector of the electromagnetic wave is
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The dispersion relation for a, low density plasma is ω2 = ω02 + c2 k2, where ω0 is the plasma frequency and c is the speed of light in free space. The relationship between the group velocity (vg) and phase velocity (vp) is
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Aspherical conductor of radius a is placed in a uniform electric field The potential at a point P(r, θ) for r > a, is given by
where, r is the distance of P from the centre O of the sphere and θ is the angle, OP makes with the Z-axis.
The charge density on the sphere at θ = 30° is
where, r is the distance of P from the centre O of the sphere and θ is the angle, OP makes with the Z-axis.
The charge density on the sphere at θ = 30° is
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A non-relativistic charged particle moves along the positive X-axis with a constant positive acceleration The particle is at the origin at t = 0. Radiation is observed at t = 0 at a distant point (0, d, 0) on the Y-axis. Which one of the following statements is correct?
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In a non-conducting medium characterized by ε = ε0, μ = μ0 and conductivity σ = 0, the electric field (in V/m) is given by The magnetic field (in A/m), is given by
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An electromagnetic wave with is travelling in free space and crosses a disc of radius 2 m placed perpendicular to the Z-axis. If E0 = 60 V/m, the average power in watt, crossing the disc along the Z-direction is
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A charged capacitor (C) is connected in series with an inductor (L). When the displacement current reduces to zero, the energy of the LC circuit is
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In an electromagnetic field, which one of the following remains invariant under Lorentz transformation?
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An electric charge +Q is placed on the surface of a solid conduction sphere of radius a. The distance measured from the centre of the sphere is denoted as r. Then,
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Consider a conducting loop of radius a and total loop resistance R placed in a region with a magnetic field B thereby enclosing a flux . The loop is connected to an electronic circuit as shown, the capacitor being initially uncharged.
If the loop is pulled out of the region of the magnetic field at a constant speed u, the final output voltage Vout is independent of
If the loop is pulled out of the region of the magnetic field at a constant speed u, the final output voltage Vout is independent of
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A conducting sphere of radius R is placed in uniform electric field directed along +Z-axis. The electric potential for outside points is given as where r is the distance from the centre and θ is the polar angle. The charge density on the surface of the sphere is
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A laser beam of wavelength 600 nm with a circular cross-section having a radius of 10 mm fails normally on a lens of radius 20 mm and focal length 10 cm. The radius of the focussed spot is approximately
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A current flows in the anticlockwise direction through a square loop of side a lying in the XOY plane with its centre at the origin. The magnetic induction at the centre of the square loop is
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The electric (E) and magnetic (B) field amplitudes associated with an electromagnetic radiation from a point source behave at a distance r from the source as
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An electron is accelerated from rest by 10.2 millionvolt. The percent increase in its mass is
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A toroidal coil has N closely-wound turns. Assume the current through the coil to be and the toroid is filled with a magnetic material of relative permittivity The magnitude of magnetic induction inside the toroid, at a radial distance r from the axis, is given by
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A particle of charge q, mass m and linear momentum enters an electromagnetic field of vector potential and scalar potential The Hamiltonian of the particle is
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Two magnetic dipoles of magnitude m each are placed in a plane as shown below. The energy of interaction is given by
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