Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
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Chapter 6.1, Problem 6.3P
(a)
To determine
The attraction force between magnetic dipoles
(b)
To determine
Force of attraction between two magnetic dipoles
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1. Fig 1, shows a hollow cylindrical conductor of radii a and b which carries a current i
uniformly spread over its cores section. a) show the the magnetic field B from points
inside the body of the conductor is given by B={uoi/27(b²-a)} {(r2-a)/r}. And check
the case when a=0. b) Make a rough plot at the general behavior of B(r) from r=0 to
infinite.
[r-current
Fig. 1
Figure 6.20 shows a metal rod PQ resting on the smooth rails AB and positioned between
the poles of a permanent magnet. The rails, the rod, and the magnetic field are in three
mutual perpendicular directions. A galvanometer G connects the rails through a switch K.
Length of the rod = 15 cm, B = 0.50 T, resistance of the closed loop containing the rod
= 9.0 m2. Assume the field to be uniform.
(a) Suppose K is open and the rod is moved with a speed of 12 cm s-1 in the direction
shown. Give the polarity and magnitude of the induced emf.
S
(b) Is there an excess charge built up at the ends of the rods when
K is open? What if K is closed?
-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.
Chapter 6 Solutions
Introduction to Electrodynamics
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- Consider problem. Use the i-j-k coordinate system. Question 1 In figure 1.1, find the direction of the Magnetic force. However, take consideration that the moving charge is positive. Figure 1.1 x B. B (c) (d) • Vout Vin (e)arrow_forwardA beam of electrons whose kinetic energy is K emerges from a thin-foil "window" at the end of an accelerator tube. A metal plate at distance d from this window is perpendicular to the direction of the emerging beam, as shown in Fig. 1. (a) Show that we can prevent the beam from hitting the plate if we apply a uniform magnetic 2mK field such that in which m and e are the electron mass and charge. (b) How should B be oriented? Foil window Electron beam Plate Tube d- Fig. 1arrow_forwardThere is a long cylinder with radius of R, and magnetization of M = Mopî for parrow_forwardA current-carrying wire hangs off a table as shown. What is the dipole moment of the fl magnet pushing it? The magnet is z = 1 cm from the wire. Assume that the push ILBmagnet is approximately equal to the weight of the wire segment mg. The segment is of length L = 2 cm, current I= 1 amp, mass m = 3 g. Also, use the approximate magnetic field for a bar magnet, Bmagnet O 7.4 Am² O None of these. O 7.4 x 10-6 Am² O 7.4 x 10° Am² = но 2н 4Tarrow_forwardQuestion A7 A wire ring of radius a, is placed in an external uniform magnetic field as shown in figure 4 B = B₂+ B₂ where B < 0 and By < 0, and carrying a clock-wise current I. a) Apply the right-hand rule and find the direction of the magnetic moment vector, . b) Derive an expression for the magnitude of the torque on the loop. X Figure 4: A wire ring in an external magnetic field || - [1 marks] marks]arrow_forwardA long coaxial cable carries current / (the current flows down the surface of the inner cylinder, radius a, and back along the outer cylinder, radius b) as shown in Fig. 7.39. Find the magnetic energy stored in a section of length I. b Figure 7.39 Assume that the two conductors are held at potential difference V and calculate the energy per unit time transported down the cables given above.arrow_forwardQ. # 2: A circular loop of radius “r" is fixed to a rotation axis along the z-direction, as shown in Fig. 2. so that the plane of the loop is always perpendicular to the xy plane. The loop is rotating about the constant angular velocity “QL" directed along the z-axis; at t = 0, the loop lies in the zy plane. Given a uniform and constant externally magnetic field B = B(cos a į + sin a i), evaluate the magnetic flux øm (t) through the loop and emf induced in the loop. 1odtarrow_forwardSolve 5,6 & 7. Use the following constants if necessary. Coulomb constant, k = 8.987×10^9 N⋅m^2/C^2 . Vacuum permitivity, ϵ0= 8.854×10^−12 F/m. Magnetic Permeability of vacuum, μ0 = 12.566370614356×10^−7 H/m. Magnitude of the Charge of one electron, e = −1.60217662×10^−19 C. Mass of one electron, m_e = 9.10938356×10^−31 kg. Unless specified otherwise, each symbol carries their usual meaning. For example, μC means microcoulomb .arrow_forwardA uniform magnetic field B has constant strength b teslas in the z-direction [i.e., B = (0, 0, b) ] (a) Verify that A = Bxr is a vector potential for B, where r = (x, y, 0) (b) Use the Stokes theorem to calculate the flux of B through the rectangle with vertices A, B, C, and D in Figure 17. A Flux(B) = = D B FIGURE 17 A = (8,0,1), B = (8,5, 0), C = (0,5, 0), D = (0, 0, 1), F = (8,0,0)arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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