The area shown is the boundary of a magnetic field directed in the positive z di

Question

The area shown is the boundary of a magnetic field directed in the positive z direction. An electron with a velocity along the x-axis enters the field at coordinates (x, y) = (?5 m, 0) and exits 0.43 ?s later at point A whose coordinates are (x, y) = (0, 5 m).

What is the magnitude of B? ? The mass of the electron is 9.109 10?31 kg and the elemental charge is ?1.602 10?19 C.

Answer in units of microT.

The area shown is the boundary of a magnetic field directed in the positive z direction. An electron with a velocity along the x-axis enters the field at coordinates (x, y) = (?5 m, 0) and exits 0.43 ?s later at point A whose coordinates are (x, y) = (0, 5 m). What is the magnitude of B? ? The mass of the electron is 9.109 ½ 10?31 kg and the elemental charge is ?1.602 10?19 C. Answer in units of microT.

Explanation / Answer

charge always constitutes circular motion in presence of magnetic field when it's motion is perpendicular to the direction of megnetic field therefore,

from the information one can say that , radius of the motion of the electron is = 5 m

accrding to theory of cyclotrone

r = (mv) / (q*B)

therefore,

B = (mv) / (qr)

B = (9.1*10^(-31) * v ) / (1.6*10^(-19) * 5)

v = quarter circile ' time taken

v = ( ( 2*pi*5 ) / 4 ) / 0.43 m/s

therefore

B = (9.1*10^(-31) * ( ( ( 2*pi*5 ) / 4 ) / 0.43) ) / (1.6*10^(-19) * 5)

B = 8.9339*10^(-6) micro Tesla

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