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The center of a bar magnet whose magnetic dipole moment is 〈8,0,0〉‼îâ‹…m2is located at the origin. A second bar magnet whose magnetic dipole moment is 〈3,0,0〉‼îâ‹…m2is located at x=0.12″¾. 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‼îâ‹…m2at location 0,0,0and μ2→=3,0,0‼îâ‹…m2at location 0.12,0,0″¾0.12,0,0″¾

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 â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â‹¯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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We will consider the possibility that a free electron actedon by an electric field could gain enough energy to ionize anair molecule in a collision. (a) Consider an electron that startsfrom rest in a region where there is an electric field (due to somecharged objects nearby) whose magnitude is nearly constant. Ifthe 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/m at 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.

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