An electron is moving in the vicinity of a long, straight wire that lies along t

Question

An electron is moving in the vicinity of a long, straight wire that lies along the x -axis. The wire has a constant current of 8.80 A in the -x -direction. At an instant when the electron is at point (0, 0.200 m , 0) and the electron's velocity is v = (5.00 × 104 m/s )i^ (3.00 × 104 m/s )j^ .

a.   

What is the force that the wire exerts on the electron?

Enter the x , y , and z components of the force separated by commas. (Fx , Fy , Fz = ? )

b.

Calculate the magnitude of this force.

Express your answer with the appropriate units. (F = ? including unit of F)

Please help. Thanks

Explanation / Answer

For the wire, magnetic field due to the wire at point ( 0 , 0.2 , 0 ) :

B = - u*I/(2*pi*r) k <------------ it is directed in -k direction

So, B = -1.26*10^-6*8.8/(2*pi*0.2) k

= -8.82*10^-6 k

So, magntic force, F = q*(v x B) = (-1.6*10^-19)*((5i - 3j)*10^4 x (-8.82*10^-6) k )

= (1.6*10^-19*8.82*10^-6*10^4)*{ (5i - 3j) x k }

= 1.41*10^-20*(-5j - 3 i)

= (-4.23*10^-20) i - (7.05*10^-20) j + 0 k

b)

magnitude of this force , | F | = sqrt(4.23^2 + 7.05^2)*10^-20

= 8.22*10^-20 N

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