Questions and Answers of Electrodynamics

Prove, by means of the divergence theorem in four dimensions or otherwise, that for source-free electromagnetic fields confined to a finite region of space, the 3-space integrals of Θ00 and Θ0i
Source-free electromagnetic fields exist in a localized region of space. Consider the various conservation laws that are contained in the integral of ∂αMαβγ = 0 over all space, where Mαβγ is
In Figure, a ray of light is perpendicular to the face ab of a glass prism (n = 1.52). Find the largest value for the angle ф so that the ray is totally reflected at face
Light that is traveling in water (with an index of refraction of 1.33) is incident on a plate of glass (with index of refraction 1.53). At what angle of incidence does the reflected light end up
(a) Prove that a ray of light incident on the surface of a sheet of plate glass of thickness t emerges from the opposite face parallel to its initial direction but displaced sideways, as in
A helium-neon laser, radiating at 632.8 nm, has a power output of 3.0 mW. The beam diverges (spreads) at angle θ = 0.17 mrad (Figure).(a) What is the intensity of the beam 40 m from the
Iron atoms have been detected in the sun’s outer atmosphere, some with many of their electrons stripped away. What is the net electric charge (in coulombs) of an iron atom with 26 protons and 7
Consider three identical metal spheres, A, B, and C. Sphere A carries a charge of +5q. Sphere B carries a charge of -q. Sphere C carries no net charge. Spheres A and B are touched together and then
Two spherical objects are separated by a distance that is 1.80 × 10-3 m. The objects are initially electrically neutral and are very small compared to the distance between them. Each object acquires
Two very small spheres are initially neutral and separated by a distance of 0.50 m. suppose that 3.0 × 1013 electrons are removed from one sphere and placed on the other.(a) What is the magnitude of
Two tiny spheres have the same mass and carry charges of the same magnitude. The mass of each sphere is 2.0 × 10-6 kg. The gravitational force that each sphere exerts on the other is balanced by the
Two particles, with identical positive charges and a separation of 2.60 × 10-2 m, are released from rest. Immediately after the release, particle 1 has an acceleration a→1 whose magnitude is 4.60
In the rectangle in the drawing, a charge is to be placed at the empty corner to make the net force on the charge at corner A point along the vertical direction. What charge (magnitude and algebraic
A small spherical insulator of mass 8.00 Ã— 10-2 kg and charge +0.600 ÂµC is hung by a thread of negligible mass. A charge of -0.900 ÂµC is held 0.150 m away from the sphere and directly to
At a distance r1 from a point charge, the magnitude of the electric field created by the charge is 248 N/C. At a distance r2 from the charge, the field has a magnitude of 132 N/C. Find the ratio
A long, thin rod (length = 4.0 m) lies along the x-axis, with its midpoint at the origin. In a vacuum, a -8.0 µC point charge is fixed to one end of the rod, and a +8.0 µC point charge is fixed to
A tiny ball (mass = 0.012 kg) carries a charge of -18 µC. What electric field (magnitude and direction) is needed to cause the ball to float above the ground?
Two point charges are located along the x-axis: q1= +6.0 µC at x1 = +4.0 cm, and q2 = +6.0µC at x2 = -4.0 cm. Two other charges are located on the y-axis: q3 = +3.0 µC at y3 = +5.0 cm and q4 =
Two point charges of the same magnitude but opposite signs are fixed to either end of the base of an isosceles triangle, as the drawing shows. The electric field at the midpoint M between the charges
The drawing shows an edge-on view of two planar surfaces that intersect and are mutually perpendicular. Surface 1 has an area of 1.7m2, while surface 2 has an area of 3.2 m2. The electric field
A cube is located with one corner situated at the origin of an x, y, z coordinate system. One of the cubes faces lies in the x, y plane, another in the y, z plane, and another in the x, z plane. In
Two charges are placed on the x-axis. One of the charges (q1 = +8.5 µC) is at x1 = +3.0 cm and the other (q2 = -21 µC) is at x1 = +9.0 cm. Find the net electric field (magnitude and direction)
Two small objects, A and B, are fixed in place and separated by 3.00 cm in a vacuum. Object A has a charge of -2.00 µC, and object B has a charge of +2.00 µC. How many electrons must be removed
At three corners of a rectangle (length = 2d, height = d), the following charges are located: +q1 (upper left corner), +q2 (lower right corner), and -q (lower left corner). The net electric field at

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