An electron passes through a point 2.79cm from a long straight wire as it moves

Question

An electron passes through a point 2.79cm from a long straight wire as it moves at 35.5% of the speed of light perpendicularly toward the wire. The wire carries a current of 13.1 A. Find the magnitude of the electron's acceleration at that point.

An electron passes through a point 2.79 cm from a long straight wire as it moves at 35.5% of the speed of light perpendicularly toward the wire. The wire carries a current of 13.1 A. Find the magnitude of the electron's acceleration at that point. Number The electron moves in the magnetic field created by the current in the wire. The resulting magnetic force causes the electron to accelerate. How do the current and the distance from the wire relate to the magnetic field? How do the magnetic field and the electron's speed relate to the magnetic force on the electron? How does this force relate to the electron's acceleration? The elementary charge is 1.602 x 10 C, the electron's mass is 19 9.109 -31 kg, the speed of light is 2.998 x108 m/s, and the vacuum permeability constant has the value 4m x 10-7 T. m/A.

Explanation / Answer

The magnetic field produced by a long straight wire is given by

(Vaccum permeability constant)*I/(2*pi*r); where R is the radial distance from the wire. Substituting we can find the magnetic field B.
B = (4pi x 10^-7)*13.1/(2*pi*2.79*10^-2) = 93 mT (approximately)

The force exerted upon the electron is given by

F = q*v*B = (1.602 x 10^-19)*(.355*2.998 x 10^8)*(.93) = 1.585 x 10^-15 N

the acceleration is simply the Force exerted on the electron divided by the mass of the electron.

a = F/m = 1.585 x 10^-15/9,109x10^-31 = 1.74 x 10^15 m/s^2

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