Start with Helmholtz for electric field for the magnetostatic case. Derive the scalar potential from Maxwell.
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Start with Helmholtz for electric field for the magnetostatic case. Derive the scalar potential from Maxwell.
Concept used:
Helmholtz theorem states that a vector can be written as sum of gradient of scalar potential and curl of a vector potential.
In magnetostatics, source of magnetic field i.e. current is steady.
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- Does the absolute value of the line integral of the magnetic field of the flat segment increase, decrease, or remain the same when the second wire is added and why5. The magnetic field is found to be B = (3(m f)f-m) for almost all space where m is an 4π 13 orienting, generating, a. b. C. time-and-space-independent vector. What are the units of m and what is it? What current distribution might generate B and prove it? What vector potential, A(7), might also generate B and prove it?A proton, that is accelerated from rest through a potential of 14.0 kV enters the velocity filter, consisting of a parallel-plate capacitor and a magnetic field, shown below. 112 The E-field between the parallel capacitor plates is 1.1.105 N/C. What B-field is required so that the protons are not deflected? (Ignore relativistic effects for high velocities.) Submit Answer Tries 0/12 Send Feedback
- At a point P on the center axis of a magnetic field created by a sufficiently long solenoid, we divide the magnetic field strength vector into a circular loop of the solenoid coil as shown below to add all the magnetic fields they create. (Let's simplify to continuous which isn't continuous). Complete this task to show that the magnetic field strength is "first image"at P point.function of r for each region below, in terms of a, b, and any physical page, uniformly distributed along its surface. Find the magnetic field as a through its cross-section, and the shell carries a total current /, into the thick wire carries a total current 1 out of the page, uniformly distributed thin cylindrical shell of radius b. (Neglect the thickness of the shell.) The A long, thick cylindrical wire of radius a is surrounded by a long. B6. 1. or numerical constants, and circle its direction. (a) B(a b) outside the shell Circle the direction: (clockwise ) (counter-clockwise ) (another direction) (there is no field)An electron and a proton, both with the same initial velocity, v, enter a region with a uniform magnetic field B out of the page, as shown. Each one undergoes semi-circular motion in the field and exits the field some distance d from the entry point. (The diagram shows the path for just one of the two particles.) Consider the following two statements and decide if they are true or false. i) The particle shown in the picture must be the negative one (the electron). ii) The distance "d" for the proton will be greater than "d " for the electron. В d. (shot with same v) i is true, but ii is false Both i and ii are false i is false, but ii is true Both i and ii are true
- A particle of charge q moves in a circle of radius a at constant angular velocity w. (Assume that the circle lies in the xy plane, centered at the origin, and at time t=0 the charge is at (a,0), on the positive x axis.) a) Find the electric and magnetic fields at the center. b) From your formula for B you obtained in a), determine the magnetic field at the center of a circular loop carrying a steady current I.A long straight cylindrical shell has an inner radius R; and an outer radius Ro. It carries a current i, uniformly distributed over its cross section. A wire is parallel to the cylinder axis, in the hollow region (r < R;). The magnetic field is zero everywhere in the hollow region. We conclude that the wire: O is on the cylinder axis and carries current i in the same direction as the current in the shell may be anywhere in the hollow region but must be carrying current i in the direction opposite to that of the current in the shell may be anywhere in the hollow region but must be carrying current i in the same direction as the current in the shell is on the cylinder axis and carries current i in the direction opposite to that of the current in the shell O does not carry any currentShow all your calculations while explaining why you do each step.An electron enters a region of uniform 0.10T magnetic field (into the page) with a kinetic energy of 100 keV. Can you calculate the radius of the curved path that it will take? (And include a diagram that shows which way the path curves).