A uniform magnetic field B has constant strength b in the z-direction [i.e., B = (0, 0, b)]. Verify that A= ½B x r is a vector potential for B, where r = (x, y, 0).
Q: Problem (1): If you have an infinite conductor wire with radius R carrying a current I, answer the…
A:
Q: Use the Biot-Savart law to calculate the magnetic field B of a ribbon with finite width (w). Suppose…
A: Determine, The magnetic field by a finite ribbon of width w using Biot-Savart law.
Q: (a) An infinite sheet of conductor in x-y plane carries a uniform surface current K KR along…
A: Step 1: Step 2: Step 3: Step 4:
Q: Example 7.10. A short solenoid (length / and radius a, with ₁ turns per unit length) lies on the…
A: In the question, it's given that Length of short solenoid = l The radius of short solenoid = a…
Q: B2 021 8
A:
Q: Please help me with this problem. A conducting rod of length A is moved with a uniform velocity v,…
A:
Q: A long, straight conducting wire with radius R is carrying cur- rent. The current density is…
A: Ampere's circuital law states that the line integral of magnetic field induction B→ around any…
Q: A particle of charge e moves in a central potential V(r) superimposed onto a uniformmagnetic field B…
A: The objective of the question is to derive the Hamiltonian for a charged particle moving in a…
Q: -A circular loop of wire, with radius R, lies in the xy plane (centered at the origin) and carries a…
A:
Q: The volume current for a solid sphere of radius R and total charge Q uniformly distributed through-…
A: Given: Jr=3Qωr sin θ4πR3ϕ^
Q: Two (1 and 2) infinite straight con- ductors run along the z axis ; they carry currents: I, = 24…
A:
Q: 9.3. A system of two conductors has a cross section given by the intersection of two circles of…
A: Here, the two loops can be regarded as two current carrying wires with cross sections of circles…
Q: A hollow cylindrical conductor of a and b radii is crossed by a uniformly distributed current.…
A:
Q: Consider a particle of charge 8.8 that is traveling with speed 90 m/s in a direction that is 19…
A: The direction of the velocity of the particle and magnetic field is drawn in the following diagram.…
Q: Consider an infinite hollow conducting cylinder of inner radius R and outer radius 3R, as shown in…
A: Ampere Circuital Law is defined by closed line integral of magnetic field at distance 'r' from the…
Q: Consider a spherical shell of inner and outer radius a and b, respectively, and conducting a uniform…
A: Given that spherical shell has an inner radius a and outer radius b.In between a to b shell has…
Q: Consider an infinite straight wire of radius R with current I. (a) Find A outside the wire. (b)…
A:
A uniform magnetic field B has constant strength b in the z-direction [i.e., B = (0, 0, b)]. Verify that A= ½B x r is a vector potential for B, where r = (x, y, 0).

Trending now
This is a popular solution!
Step by step
Solved in 2 steps

- An infinitely large plate has uniform surface charge density +o where o is a positive number. The plate moves with speed v along the x-direction. Since the charges are moving with the plate, they form a uniform two dimensional surface current density K whose value is |K| by a line of length L is I = |K|L. See Fig. 2(A) below. = ov. Namely, the electric current I passing (A) K X (B) (C) +o V V Ampere loop FIGURE 2 (a) By symmetry, the value of magnetic field B due to the current K above or below the plate is the same, and B is obviously parallel to the plate. In which direction is B pointing above the plate? Below the plate? (b) Find the value of the magnetic field B above or below the plate by Ampere's law, using the rectan- gular Ampere loop shown in the Fig. 2(B). Again, by symmetry, the values of B must be the same above or below the plate, and it must be a constant that only depends on |K| and v. Hint: Compute S B · dl´along the four segments of the Ampere loop and pay attention if…Given that A and B are hermitian operators, show that [A,[A,B]]=0Consider an infinite hollow conducting cylinder of inner radius R and outer radius 3R, as shown. The non-uniform current density J is out of the page and varies with distance r fromthe center as J=J0rk (k is k hat) where J0 is a positive constant. Calculate the magnetic field at point P (r = 2R) from the centre,(magnitude and direction). Sketch the Amperian loop.
- 13.1 The magnetic vector potential at point P(r, 0, d) due to a small antenna located at the origin is given by 50 e-jßr A, where = x + y + 2. Find E(r, 0, þ, t) and H(r, 0, þ, t) at the far field.Biot-Savart’ s Law. 2. Line x = O, y = 0, 0 ¡ z ¡ 10 m carries current 2 A along az. Calculate H at points:(a) (5,5,0)(b) (5,15,0)(c) (5,-15,0)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 current
- -A circular loop of wire, with radius R, lies in the xy plane (centered at the origin) and carries a current I running counterclockwise as viewed from the positive z axis. (a) What is its magnetic dipole moment? (b) What is the (approximate) magnetic field at points far from the origin? (c) Show that, for points on the z axis, your answer is consistent with the exact field (Ex. 5.6), when z » R.Consider an infinitely long, thick, cylindrical shell with an inner radius a and outer radius b. A current I is uniformly distributed across the shell (i.e., in the region a < r < b), coming out of the page.(a) Use Ampere’s law to derive equations for the magnitude of the magnetic field in all three regions (i.e., for 0 < r < a, a < r < b, and r > b).(b) Show that the magnetic field is continuous at r = a and r = b.