The magnetic field B due to a small current loop (which we place at the origin) is called a magnetic dipole (Figure ). Let p = (x2 + y² + z²)'/2. For p large, B = curl(A), where A = (a) Let C be a horizontal circle of radius R with center (0, 0, c), where c is large. Show that A is tangent to C. (b) Use Stokes' Theorem to calculate the flux of B through C. Current loop FIGURE
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- Suppose that a uniform magnetic field points into this screen. If a positively charged particle moves from left to right (→), in what direction does the field exert a force on the particle?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 CONTRIBUtESuppose there were an asteroid approaching the Earth-Moon system starting from rest at infinity. Under what conditions would it experience forces directing it toward a collision with the Moon rather than toward a collision with Earth? If it were on a path within a narrow cone where the field lines converge directly toward the Moon it would go there. Otherwise it would end at Earth. All the field lines converge at the Earth rather than the Moon. The field at a distance would take take it with equal probability toward the Earth or toward the Moon. The field would take it mostly through the empty space between Earth and Moon with no collision
- 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)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)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 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 currentConsider two infinitely long and parallel wires separated by distance d and carrying currents I₁ = -12. (a) Find the magnitude and direction of the vector potential A(r1,72) at a point P where r₁ and r2 represent the distances to P from wire 1 and wire 2 respectively. (b) What is the magnitude of A for r₁ = r₂? (c) What is the value of the magnetic field B for r₁ = r₂? (d) Given that B = V x A, how can you reconcile the answers to (b) and (c) above?Consider the diagram below. One wire is aligned with the x-axis and carries current I1 = 1.0 A. Another wire carries current l2 = 2.0 A out of the page at point (0,1) as shown. P(3, 1) What is the magnitude of the B-field at point P? Express your answer to the nearest nT.