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Chapter 20: Q74P (page 863)

The center of a bar magnet whose magnetic dipole moment is 〈8,0,0〉 A⋅m2is located at the origin. A second bar magnet whose magnetic dipole moment is 〈3,0,0〉 A⋅m2is located at x=0.12 m. What is the vector force on the second magnet due to the first magnet?

Short Answer

Expert verified

The vector force on the second magnet due to the first magnet is6.94×10−2 N

Step by step solution

01

Given Information

The dipole moment is given by μ1→=8,0,0 A⋅m2at location 0,0,0and μ2→=3,0,0 A⋅m2at location 0.12,0,0 m0.12,0,0 m

02

Force of Attraction and Repulsion

It is known that two magnets should attract or repel each other with a force proportional to 1r4and the attractive or repulsive force exert on a magnetic dipole moment by this magnet is given as:

F=3μ2μ04π⋅2μ1r4                 ⋯1

03

Calculate the vector force

Now substitute the value μ1=8,μ2=3and r=0.12in equation (1),

F=3μ2μ04π⋅2μ1r4=3⋅31×10−7280.124=6.94×10−2 N

Thus, the vector force on the second magnet due to the first magnet is 6.94×10−2 N.

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Most popular questions from this chapter

A metal rod of length L slides horizontally at constant speed v on frictionless insulating rails through a region of uniform upward magnetic field of magnitude B (Figure 20.124).

On a diagram, show the polarization of the rod and the direction of the Coulomb electric field inside the rod. Explain briefly. What is the magnitude of the Coulomb electric field inside the rod? What is the potential difference across the rod? What is the emf across the rod? What are the magnitude and direction of the force you have to apply to keep the rod moving at a constant speed v?

A copper wire with square cross section carries a conventional current I to the left (as in Figure 20.83). There is a magnetic field B perpendicular to the wire. Describe the direction of E⊥, the transverse electric field inside the wire due to the Hall effect, and explain briefly.

A neutral metal rod of length 60 cm falls toward the Earth. The rod is horizontal and oriented east west. (1) Which end of the rod, east or west, has excess electrons? Explain using physics diagrams. (2) At a moment when the rod’s speed is 4m/s , approximately how many excess electrons are at the negative end of the rod?

We will consider the possibility that a free electron acted on by an electric field could gain enough energy to ionize an air molecule in a collision. (a) Consider an electron that starts from rest in a region where there is an electric field (due to some charged objects nearby) whose magnitude is nearly constant. If the electron travels a distance dand the magnitude of the electric field is E,what isthe potential difference through which the electron travels? (Pay attention to signs: Is the electron traveling with the electric field or opposite to the electric field?) (b) What is the change in potential energy of the system in this process? (c) What is the change in the kinetic energy of the electron in this process? (d) We found the mean free path of an electron in air to be about 5×10-7 m, and in the previous question you calculated the energy required to knock an electron out of an atom. What is the magnitude of the electric field that would be required in order for an electron to gain sufficient kinetic energy to ionize a nitrogen molecule? (e) The electric field required to cause a spark in air is observed to be about 3×106 V/mat STP. What is the ratio of the magnitude of the field you calculated in the previous part to the observed value at STP? (f) What is it reasonable to conclude about this model of how air becomes ionized? (1) Since we used accurate numbers, this is a huge discrepancy, and the model is wrong. (2) Considering the approximations we made, this is pretty good agreement, and the model may be correct.

In Figure 20.116 a battery with known emf=K is connected to two large parallel metal plates. Each plate has a length L and width W, and the plates are a very short distance apart. The plates are surrounded by a vertical thin circular coil of radius R containing N turns through which runs a steady conventional current I. The center of the coil is at the center of the gap between the plates. At a certain instant, a proton (charge +e, mass M) travels through the center of the coil to the right with speed v, and the net force on the proton at this instant is zero (neglecting the very weak gravitational force). What are the magnitude and direction of conventional current in the coil? Explain clearly.
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