Advertisements
Advertisements
Question
Answer the following question.
Prove that the average energy density of the oscillating electric field is equal to that of the oscillating magnetic field.
Solution
Energy density in the electric field is `U_E = 1/2ε_0E^2`
Energy density in the magnetic field is `U_B = 1/(2μ_0)B^2`
We know E = Bc
`c = 1/sqrt(ε_0μ_0)`
`U_E = 1/2ε_0(cB)^2 = 1/2ε_0(1/(ε_0μ_0))B^2 = B^2/(2μ_0)`
now, `U_E = U_B`
RELATED QUESTIONS
Plot a graph showing the variation of resistivity of a conductor with temperature.
A charge Q is uniformly distributed over a large plastic plate. The electric field at a point P close to the centre of the plate is 10 V m−1. If the plastic plate is replaced by a copper plate of the same geometrical dimensions and carrying the same charge Q, the electric field at the point P will become
A metallic particle with no net charge is placed near a finite metal plate carrying a positive charge. The electric force on the particle will be
Show that there can be no net charge in a region in which the electric field is uniform at all points.
A charge Q is placed at the centre of an imaginary hemispherical surface. Using symmetry arguments and Gauss's Law, find the flux of the electric field due to this charge through the surface of the hemisphere in the following figure.
A charge Q is placed at the centre of an uncharged, hollow metallic sphere of radius a. (a) Find the surface. (b) If a charge q is put on the sphere, what would be the surface charge densities on the inner and outer surfaces? (c) Find the electric field inside the sphere at a distance x from the centre in the situations (a) and (b).
A non-conducting sheet of large surface area and thickness d contains a uniform charge distribution of density ρ. Find the electric field at a point P inside the plate, at a distance x from the central plane. Draw a qualitative graph of E against x for 0 < x < d.
One end of a 10 cm long silk thread is fixed to a large vertical surface of a charged non-conducting plate and the other end is fastened to a small ball of mass 10 g and a charge of 4.0× 10-6 C. In equilibrium, the thread makes an angle of 60° with the vertical (a) Find the tension in the string in equilibrium. (b) Suppose the ball is slightly pushed aside and released. Find the time period of the small oscillations.
Two conducting plates X and Y, each with a large surface area A (on one side), are placed parallel to each other, as shown in the following figure . Plate X is given a charge Q,whereas the other is kept neutral. Find (a) the surface charge density at the inner surface of plate X (b) the electric field at a point to the left of the plates (c) the electric field at a point in between the plates and (d) the electric field at a point to the right of the plates.
Pick out the statement which is incorrect
