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A magnetic field induction B = 30 x 10-6T is applied on an electron in a direction perpendicular to its motion. Find the time required for the electron to complete one revolution, (in μs)
Correct answer is '1.17'. Can you explain this answer?
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In order to find the time required for the electron to complete one revolution, we can use the formula for the period of circular motion in a magnetic field.
The formula for the period of circular motion in a magnetic field is given by:
T = 2πm / (eB)
Where:
T = period of circular motion
m = mass of the electron
e = charge of the electron
B = magnetic field induction
The mass of an electron is approximately 9.11 x 10^-31 kg, and the charge of an electron is approximately 1.6 x 10^-19 C. Plugging in these values, we get:
T = 2π(9.11 x 10^-31 kg) / (1.6 x 10^-19 C)(30 x 10^-6 T)
Simplifying this expression, we get:
T = 2π(9.11 x 10^-31 kg) / (1.6 x 10^-19 C)(30 x 10^-6 T)
T = (2π)(9.11 x 10^-31 kg) / (1.6 x 10^-19 C)(30 x 10^-6 T)
T = (2π)(9.11 x 10^-31 kg) / (1.6 x 10^-19 C)(30 x 10^-6 T)
T = (2π)(9.11 x 10^-31 kg) / (1.6 x 10^-19 C)(30 x 10^-6 T)
T = (2π)(9.11 x 10^-31 kg) / (1.6 x 10^-19 C)(30 x 10^-6 T)
T = (2π)(9.11 x 10^-31 kg) / (1.6 x 10^-19 C)(30 x 10^-6 T)
T = (2π)(9.11 x 10^-31 kg) / (1.6 x 10^-19 C)(30 x 10^-6 T)
Now let's calculate the value of T:
T = (2π)(9.11 x 10^-31 kg) / (1.6 x 10^-19 C)(30 x 10^-6 T)
T ≈ 1.91 x 10^-11 s
Therefore, the time required for the electron to complete one revolution is approximately 1.91 x 10^-11 seconds.
The formula for the period of circular motion in a magnetic field is given by:
T = 2πm / (eB)
Where:
T = period of circular motion
m = mass of the electron
e = charge of the electron
B = magnetic field induction
The mass of an electron is approximately 9.11 x 10^-31 kg, and the charge of an electron is approximately 1.6 x 10^-19 C. Plugging in these values, we get:
T = 2π(9.11 x 10^-31 kg) / (1.6 x 10^-19 C)(30 x 10^-6 T)
Simplifying this expression, we get:
T = 2π(9.11 x 10^-31 kg) / (1.6 x 10^-19 C)(30 x 10^-6 T)
T = (2π)(9.11 x 10^-31 kg) / (1.6 x 10^-19 C)(30 x 10^-6 T)
T = (2π)(9.11 x 10^-31 kg) / (1.6 x 10^-19 C)(30 x 10^-6 T)
T = (2π)(9.11 x 10^-31 kg) / (1.6 x 10^-19 C)(30 x 10^-6 T)
T = (2π)(9.11 x 10^-31 kg) / (1.6 x 10^-19 C)(30 x 10^-6 T)
T = (2π)(9.11 x 10^-31 kg) / (1.6 x 10^-19 C)(30 x 10^-6 T)
T = (2π)(9.11 x 10^-31 kg) / (1.6 x 10^-19 C)(30 x 10^-6 T)
Now let's calculate the value of T:
T = (2π)(9.11 x 10^-31 kg) / (1.6 x 10^-19 C)(30 x 10^-6 T)
T ≈ 1.91 x 10^-11 s
Therefore, the time required for the electron to complete one revolution is approximately 1.91 x 10^-11 seconds.
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