An electron is moving along the z-axis in the positive direction with a velocity

Question

An electron is moving along the z-axis in the positive direction with a velocity of 3 × 107 m/s. If it is currently at the origin, answer the following questions. a) What is the magnetic field at a distance of 50 m along the positive x-axis? Give both magnitude and direction: b) What is the magnetic force experienced by a proton located at this position? The proton has a velocity of 8 × 107 m/s and is moving in the +x direction. c) What is the magnetic field at a distance of 50 m along the positive z-axis? Give both magnitude and direction.

Explanation / Answer

a) B = (u0 q / 4pi) ( v x r) / |r|^3

q = - 1.6 x 10^-19

v = 3 x 10^7 m/s k

r = 50 x 10^-6 m i

B = (4pi x 10^-7 x -1.6 x 10^-19 / 4pi) ( 3x10^7 k X 50E-6 i ) / (50 x 10^-6)^3

B = - 1.92 x 10^-10 T j

field is 1.92 x 10^-10 T along negative y axis.

B) F = q ( v x B)

v = 8 x 10^7 i

F = (1.6E-19) ( 8E+7 i X -1.92E-10 j )

= - 2.458 x 10^-21 N k

C) due to electron :

Be = (4pi x 10^-7 x -1.6 x 10^-19 / 4pi) ( 3x10^7 k X 50E-6 k ) / (50 x 10^-6)^3

B = 0

due to proton:

Bp = (4pi x 10^-7 x 1.6 x 10^-19 / 4pi) ( 8 x10^7 i X 50E-6 k ) / (50 x 10^-6)^3

B = - 5.12 x 10^-10 T j

magnitude = 5.12 x 10^-10 T

direction => along negative y axis.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.