The astronomical object 4U0142 + 61 has the distinction of creating the most pow

Question

The astronomical object 4U0142 + 61 has the distinction of creating the most powerful magnetic field ever observed. This object is referred to as "magnetar" (a subclass of pulsars), and its magnetic field is 1.3 1015 times greater than the Earth's magnetic field.
(a) Suppose a 4.6 m straight wire carrying a current of 2.2 A is placed in this magnetic field at an angle of 75° to the field lines. What force does this wire experience?
1 N

(b) A field this strong can significantly change the behavior of an atom. To see this, consider an electron moving with a speed of 3.1 106 m/s. Compare the maximum magnetic force exerted on the electron to the electric force a proton exerts on an electron in a hydrogen atom. The radius of the hydrogen atom is 5.29 10-11 m.
max force on electron
force of proton on electron
=

Explanation / Answer

Part A)

This answer strongly depends on what your book uses for the value of the earths magnetic field. I will use an accepted value of 0.5 X 10-4 T. If your book uses something different, the answers will be off, but the procedure is valid. Just plug in the number your book uses.

The equation to use is

F = BILsin

F = (.5 X 10-4)(1.3 X 1015)(2.2)(4.6)(sin 75)

F = 6.35 X 1011 N

Part B)

This field would exert a force on a electron found by

F = qvB

F = (1.6 X 10-19)(3.1 X 106)(.5 X 10-4)(1.3 X 1015) = .032 N

The force a proton everts on an electron is a centripetal force found by

mv2/r

(9.11 X 10-31)(3.1 X 106)2/(5.29 X 10-11)

The force is 1.65 X 10-7 N

Therefore, that magnetic field would exert a force that is 1.93 X 105 times stronger that the force holding the electrons in orbit. That force would therefore not allow atoms to exist as we know them.

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