A long, straight wire lies carries a current I = 12.0 A in the direction, as sho

Question

A long, straight wire lies carries a current I = 12.0 A in the direction, as shown in the diagram. An electron is fired parallel to this wire with a velocity of 4.50 times 10^5 m/s in the same direction as the current, 1.80 cm from the wire. (a) Find the magnitude and direction of the magnetic field at the location of the electron. Specify the direction using the coordinate system sketched in the diagram. (b) Find the magnitude and direction of the acceleration of the electron. (c) Find the magnitude and direction of a uniform electric field that will allow the electron to travel parallel to the wire. Explain your reasoning. (You can safely assume that gravity is negligible.)

Explanation / Answer

part a )

B = uo*I/2pi*r

r = 1.8 cm = 1.8 x 10^-2 m

I = 12 A

uo = 4pi x 10^-7

B = 1.33 x 10^-4

part b )

F = qvB

F = ma

a = qvB/m

m = mass of electron = 9.11 x 10^-31 kg

q = 1.6 x 10^-19 C

a = 1.054 x 10^13 m/s^2

aay from the wire

part c )

E = vB = 60 N

here we can neglect gravity because Fg = mg = 9.11 x 10^-31 * 9.8 around 10^-29 N

Fe = qE = 1.6 x 10^-19 *60 = 9.6 x 10^-18

Fe >>Fg so we can neglect gravity

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