5. Two electrons are moving in concentric circular orbits of the same radius, 8.5 x 10-4 m with the same speed, 3 x 107 m s 1 in mutually perpendicular planes. Calculate the magnitude and direction of the resultant magnetic field at the centre of the orbit. (Given: Mass of electron = 9 × 10-31 kg, charge of electron-1.6 × 10-19 C).
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Answer:
The magnetic field due to the circular coil at the center is given by,
B
=
4π
μ
0
r
2πni
The magnetic field due to the first circular coil is given by,
B
1
=
4π
μ
0
r
1
2πni
1
The magnetic field due to the second circular coil is given by,
B
2
=−
4π
μ
0
r
2
2πni
2
The resultant magnetic field is given by,
B=B
1
+B
2
B=
4π
μ
0
r
1
2πni
1
−
4π
μ
0
r
2
2πni
2
B=
2
μ
0
[
r
1
ni
1
−
r
2
ni
2
]
B=
2
μ
0
[
0.20
10×0.2
−
0.40
10×40
]
B=0
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