A charged particle is moving with relativistic speed in a static, uniform electric field E-(E,0,0) along the x-axis. Assume that the particle is initially at rest so that the motion is effectively one-dimensional. Express the energy of the particle as a function of instantaneous position x(t) and solve the resulting equation of motion to obtain the value of x(t).
The energy of a charged particle in an electric field is given by the sum of its kinetic energy and potential energy. For a particle with charge \(q\) moving in a static, uniform electric field \(\mathbf{E} = (E, 0, 0)\), the potential energy at position \(x(t)\) is \(U(x) = -qEx(t)\). The kinetic energy ___ ________ ________ _______ ______ ______ _________.
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Explain the concept of displacement current. An infinitely long perfectly conducting cylindrical wire of radius a is surrounded by a coaxial perfectly conducting cylindrical tube of radius b. The potential difference between the wire and the tube is V(t). Compute V x B in the region between the wire and the tube.
At time t= 0, a particle having charge q is placed at rest at the point (0, 0) in a region of crossed uniform static electric and magnetic fields specified by Describe the motion of the particle and show that the motion is periodic.
Obtain expressions for electric and magnetic fields in terms of scalar and vector potentials using homogeneous Maxwell's equations.
A circular wire loop of radius ris kept in the x-y plane in a region of uniform magnetic field pointing in the z-direction. The magnitude of the magnetic field is held constant at B=0 from time t=0 to time.t=t1 Thereafter, the magnetic field is increased at constant rate from B=0at time t=t2 to BB till time f-12 and then reduced at a constant rate from B= Bo to B=0 at time t=t3. a) Compute the magnetic flux through the circular wire loop as a function of time. b) Compute the induced emf in the circular loop as a function of time. c) Plot the magnetic flux and induced emf as a function of time.
Using Fourier integral theorem, obtain the expression for the velocity of a wave packet in a medium for which the dispersion relation is given as
A plane electromagnetic wave propagating in z-direction is incident on the boundary between two linear dielectric media. The boundary is in the x-y plane perpendicular to the direction of propagation of the wave. Using the boundary conditions on the electric and magnetic fields associated with the wave, show that if the incident wave is plane polarised then the reflected and transmitted waves also have the same polarisation.
Show that the retarded scalar potential given by
and the retarded vector potential given by
,
satisfy the Lorentz gauge condition.