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An electron with a speed of 1.8 x 106 m/s is moving in a circular orbit in a uniform magnetic field of 10-4 Wb/m², the radius of the circular path of the electron is
- a)10.63 m
- b)1.063 m
- c)106.3 m
- d)0.1063 m
Correct answer is option 'D'. Can you explain this answer?
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An electron with a speed of 1.8 x 106m/s is moving in a circular orbit...
4. 0.1063 m
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An electron with a speed of 1.8 x 106m/s is moving in a circular orbit...
The magnetic field is given in units of Weber per meter (Wb/m), which is equivalent to Tesla (T).
The equation for the centripetal force acting on a charged particle in a magnetic field is:
F = Bqv
Where:
F = centripetal force
B = magnetic field strength
q = charge of the particle
v = velocity of the particle
Since the electron has a negative charge, it will experience a force perpendicular to its velocity and the magnetic field direction, according to the right-hand rule.
The centripetal force is provided by the electrostatic force between the electron and the nucleus of the atom it is orbiting. Therefore, we can equate these two forces:
F = F electrostatic
Bqv = mv^2/r
Where:
m = mass of the electron
r = radius of the circular orbit
We can rearrange this equation to solve for the radius:
r = mv / Bq
Substituting the given values:
m = 9.11 x 10^-31 kg (mass of electron)
v = 1.8 x 10^6 m/s
B = 10^-4 T
q = -1.6 x 10^-19 C (charge of electron)
r = (9.11 x 10^-31 kg) x (1.8 x 10^6 m/s) / (10^-4 T x -1.6 x 10^-19 C)
r = 0.0607 meters
Therefore, the radius of the circular orbit is approximately 0.0607 meters.
The equation for the centripetal force acting on a charged particle in a magnetic field is:
F = Bqv
Where:
F = centripetal force
B = magnetic field strength
q = charge of the particle
v = velocity of the particle
Since the electron has a negative charge, it will experience a force perpendicular to its velocity and the magnetic field direction, according to the right-hand rule.
The centripetal force is provided by the electrostatic force between the electron and the nucleus of the atom it is orbiting. Therefore, we can equate these two forces:
F = F electrostatic
Bqv = mv^2/r
Where:
m = mass of the electron
r = radius of the circular orbit
We can rearrange this equation to solve for the radius:
r = mv / Bq
Substituting the given values:
m = 9.11 x 10^-31 kg (mass of electron)
v = 1.8 x 10^6 m/s
B = 10^-4 T
q = -1.6 x 10^-19 C (charge of electron)
r = (9.11 x 10^-31 kg) x (1.8 x 10^6 m/s) / (10^-4 T x -1.6 x 10^-19 C)
r = 0.0607 meters
Therefore, the radius of the circular orbit is approximately 0.0607 meters.
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An electron with a speed of 1.8 x 106m/s is moving in a circular orbit...
The force experienced by the electron due to the magnetic field is given by:
F = qvB
where q is the charge of the electron, v is its velocity, and B is the magnetic field strength.
Substituting the given values, we get:
F = (1.6 x 10^-19 C)(1.8 x 10^6 m/s)(10^-4 Wb/m)
F = 2.88 x 10^-13 N
This force provides the necessary centripetal force to keep the electron in its circular orbit. The centripetal force is given by:
F = mv^2/r
where m is the mass of the electron and r is the radius of the orbit.
Equating the two forces, we get:
mv^2/r = qvB
Solving for r, we get:
r = mv/qB
Substituting the values of m, v, q, and B, we get:
r = (9.11 x 10^-31 kg)(1.8 x 10^6 m/s)/(1.6 x 10^-19 C)(10^-4 Wb/m)
r = 1.035 x 10^-2 m
Therefore, the radius of the circular orbit of the electron is 1.035 x 10^-2 m.
F = qvB
where q is the charge of the electron, v is its velocity, and B is the magnetic field strength.
Substituting the given values, we get:
F = (1.6 x 10^-19 C)(1.8 x 10^6 m/s)(10^-4 Wb/m)
F = 2.88 x 10^-13 N
This force provides the necessary centripetal force to keep the electron in its circular orbit. The centripetal force is given by:
F = mv^2/r
where m is the mass of the electron and r is the radius of the orbit.
Equating the two forces, we get:
mv^2/r = qvB
Solving for r, we get:
r = mv/qB
Substituting the values of m, v, q, and B, we get:
r = (9.11 x 10^-31 kg)(1.8 x 10^6 m/s)/(1.6 x 10^-19 C)(10^-4 Wb/m)
r = 1.035 x 10^-2 m
Therefore, the radius of the circular orbit of the electron is 1.035 x 10^-2 m.
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An electron with a speed of 1.8 x 106m/s is moving in a circular orbit in a uniform magnetic field of 10-4Wb/m², the radius of the circular path of the electron isa)10.63 mb)1.063 mc)106.3 md)0.1063 mCorrect answer is option 'D'. Can you explain this answer? for Class 12 2025 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about An electron with a speed of 1.8 x 106m/s is moving in a circular orbit in a uniform magnetic field of 10-4Wb/m², the radius of the circular path of the electron isa)10.63 mb)1.063 mc)106.3 md)0.1063 mCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 12 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An electron with a speed of 1.8 x 106m/s is moving in a circular orbit in a uniform magnetic field of 10-4Wb/m², the radius of the circular path of the electron isa)10.63 mb)1.063 mc)106.3 md)0.1063 mCorrect answer is option 'D'. Can you explain this answer?.
An electron with a speed of 1.8 x 106m/s is moving in a circular orbit in a uniform magnetic field of 10-4Wb/m², the radius of the circular path of the electron isa)10.63 mb)1.063 mc)106.3 md)0.1063 mCorrect answer is option 'D'. Can you explain this answer? for Class 12 2025 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about An electron with a speed of 1.8 x 106m/s is moving in a circular orbit in a uniform magnetic field of 10-4Wb/m², the radius of the circular path of the electron isa)10.63 mb)1.063 mc)106.3 md)0.1063 mCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 12 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An electron with a speed of 1.8 x 106m/s is moving in a circular orbit in a uniform magnetic field of 10-4Wb/m², the radius of the circular path of the electron isa)10.63 mb)1.063 mc)106.3 md)0.1063 mCorrect answer is option 'D'. Can you explain this answer?.
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