Write the Electric and Magnetic field in forms of two invariants such that
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Write the Electric and Magnetic field in forms of two invariants such that
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- A proton with velocity vo enters a region containing magnetic (B) and gravitational (g) fields. Assume the fields are everywhere uniform, with g pointed "down" and B "into the page" as shown in the image below. Starting at the point labeled vo, provide a sketch of the trajectory of the proton subject to the two forces. Include enough of the trajectory in your sketch to highlight all key aspects of the motion.please solve in a detailed and concise mannerA point charge q moves with velocity v = vx ex + Vy Ey in a region where there is a constant electric field E = Eo ex and a constant magnetic field B Bo ez. Determine expressions for Vx and Vy if the net electromagnetic force on the charge vanishes. =
- An ideal capacitor has two conducting plate that separated by a distance L, where two plates can have opposite charges (+q and -q). However, in a capacitor, current can flow through this device. Maxwell inserted one term la = €0 to solve the problem. Prove this term is indeed current (has the unit dt of Coulomb/sec).A coaxial cable consists of two very long cylindrical tubes, separated by linear insulating material of mag- netic susceptibility Xm, A current I flows down the inner conductor and returns along the outer one. The current is uniformly distributed in each case. Find the magnetic field in the region between the tubes.The magnetic field lines inside linear media “reflect” at the interface. Assuming there is no free current flowing at the interface and the permeability of the two media are u1 and u2 respectively, find tan theta2 in terms of u1, u2 and theta 1.
- Determine the phasor forms of the following instantaneous vector fields:(a) H = −10cos(106t + π/3)ax(b) E = 4cos(4y)cos(104t − 2x)az(c) D = 5sin(104t + π/3)ax − 8cos(104t − π/4)ayA solenoid of radius r = 1.25 cm and length = 26.0 cm has 280 turns and carries 12.0 A. R b (a) Calculate the flux through the surface of a disk-shaped area of radius R = 5.00 cm that is positioned perpendicular to and centered on the axis of the solenoid as in the figure (a) above. μWb μWb (b) Figure (b) above shows an enlarged end view of the same solenoid. Calculate the flux through the tan area, which is an annulus with an inner radius of a = 0.400 cm and outer radius of b = 0.800 cm.Consider the circuit in the figure (b). The curved segments are arcs of circles of angle 35o and radii a = 12 cm and b = 6 cm. The straight segments are along radii. Find the magnetic field B at point P ( the center of curvature), assuming a current of 1 A clockwise in the circuit. (Positive out of page and negative into page) ONLY THE CURVED SEGMENTS CONTRIBUtE
- do P(0,0.2) R FIGURE 3-11 A uniformly charged disk (Example 3-8).A uniform magentic field is directed horizonally torward the north, and a positive charge is moving west through this field. Is there a magnetic force on this charge and if so, in what direction?Consider a current-carrying wire of length L carrying a current of magnitude I from left to right. What is the magnetic field contribution dB⃗ at point P, with coordinates (x,y), due to the current element dl→ at point A, with coordinates (a,0)? Assume that y is positive.