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A uniform magnetic field acts at right angles to the direction of motion of electrons. As a result, the electron moves in a circular path of radius 2 cm. If the speed of electron is doubled, then the radius of the circular path will be
- a)2.0 cm
- b)0.5 cm
- c)4.0 cm
- d)1.0 cm
Correct answer is option 'C'. Can you explain this answer?
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A uniform magnetic field acts at right angles to the direction of mot...
As v is doubled, the radius also becomes double. Hence radius = 2 x 2 = 4 cm
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A uniform magnetic field acts at right angles to the direction of mot...
Concept:
When a charged particle moves perpendicular to a uniform magnetic field, it experiences a magnetic force that acts as a centripetal force, causing the particle to move in a circular path. The radius of this circular path can be determined using the equation:
r = mv/qB
where r is the radius of the circular path, m is the mass of the charged particle, v is its velocity, q is its charge, and B is the magnitude of the magnetic field.
Given:
Radius of the circular path, r = 2 cm
Velocity of the electron, v = v
Charge of the electron, q = e (elementary charge)
Magnetic field, B = B
Calculation:
From the given information, we can write the equation as follows:
r = mv/qB
Since the electron's mass (m) and charge (q) are constant, we can rearrange the equation as follows:
r ∝ v/B
This means that the radius of the circular path is directly proportional to the velocity of the electron and inversely proportional to the magnitude of the magnetic field.
Effect of Doubling the Velocity:
If the speed of the electron is doubled, the new velocity is 2v. Substituting this value into the equation, we get:
r' = 2v/B
Comparing this with the original equation, we can see that the new radius (r') is twice the original radius (r). Therefore, the radius of the circular path will be 4 cm.
Conclusion:
When the speed of the electron is doubled, the radius of the circular path increases by a factor of 2. Hence, the correct answer is option (c) 4.0 cm.
When a charged particle moves perpendicular to a uniform magnetic field, it experiences a magnetic force that acts as a centripetal force, causing the particle to move in a circular path. The radius of this circular path can be determined using the equation:
r = mv/qB
where r is the radius of the circular path, m is the mass of the charged particle, v is its velocity, q is its charge, and B is the magnitude of the magnetic field.
Given:
Radius of the circular path, r = 2 cm
Velocity of the electron, v = v
Charge of the electron, q = e (elementary charge)
Magnetic field, B = B
Calculation:
From the given information, we can write the equation as follows:
r = mv/qB
Since the electron's mass (m) and charge (q) are constant, we can rearrange the equation as follows:
r ∝ v/B
This means that the radius of the circular path is directly proportional to the velocity of the electron and inversely proportional to the magnitude of the magnetic field.
Effect of Doubling the Velocity:
If the speed of the electron is doubled, the new velocity is 2v. Substituting this value into the equation, we get:
r' = 2v/B
Comparing this with the original equation, we can see that the new radius (r') is twice the original radius (r). Therefore, the radius of the circular path will be 4 cm.
Conclusion:
When the speed of the electron is doubled, the radius of the circular path increases by a factor of 2. Hence, the correct answer is option (c) 4.0 cm.
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A uniform magnetic field acts at right angles to the direction of motion of electrons. As a result, the electron moves in a circular path of radius 2 cm. If the speed of electron is doubled, then the radius of the circular path will bea)2.0 cmb)0.5 cmc)4.0 cmd)1.0 cmCorrect answer is option 'C'. Can you explain this answer?
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