The radius of an atom is 10^-10 m,if an electron of mass 9×10^-31 kg has an angular velocity of 8π radsecs.if the period of the electron is 10^-15 secs.
Find the current generated by the Moving electron.(take electron charge,q=1.6×10^-19C
A.1.6×10 Amp
B.1.6×10^-4 Amp
C.1.6×10^-3 Amp
D.1.6×10^-2 Amp?
How did you get the answer please show working
What's the correct answer to this question
To find the current generated by the moving electron, we can use the formula for current:
I = q/T
where I is the current, q is the charge of the electron, and T is the period of the electron.
Given:
Charge of the electron, q = 1.6 x 10^-19 C
Period of the electron, T = 10^-15 s
Plugging in these values into the formula, we get:
I = (1.6 x 10^-19 C) / (10^-15 s)
I = (1.6 x 10^-19 C) * (1 s / 10^-15 s)
I = 1.6 x 10^-19 C * 10^15 s
I = 1.6 x 10^-4 A
Therefore, the current generated by the moving electron is 1.6 x 10^-4 Amps.
Option B. 1.6 x 10^-4 Amps is the correct answer.
To find the current generated by the moving electron, we can use the formula for current, which is given by:
I = q * v,
where I is the current, q is the charge, and v is the velocity of the charged particle.
From the given information, the charge of an electron is q = 1.6×10^-19 C, and the period of the electron is T = 10^-15 s. We know that the period of a particle moving in a circular path is related to its angular velocity by the formula:
T = 2π / ω,
where ω is the angular velocity.
In this case, we are given the angular velocity, so we can rearrange this formula to solve for T:
ω = 2π / T.
Substituting the given values, we can calculate the angular velocity as:
ω = 2π / (10^-15) = 2π x 10^15 rad/s.
Now, since the electron is moving in a circular path with a radius r = 10^-10 m, we can use the formula for the velocity of an object moving in a circular path:
v = ω * r.
Substituting the values, we have:
v = (2π x 10^15 rad/s) * (10^-10 m) = 2π x 10^5 m/s.
Finally, we can calculate the current using the formula:
I = q * v,
I = (1.6×10^-19 C) * (2π x 10^5 m/s).
Evaluating this expression, we can find:
I = 1.6 x 2π x 10^-14 A.
Simplifying, we get:
I = 3.2π x 10^-14 A.
To find the answer, we need to convert this value to scientific notation:
I ≈ 3.2 x 3.14 x 10^-14 A.
Rounding to the nearest option, we find that the current is approximately 1.6 x 10^-13 A.
None of the given options are in this range, so please make sure the options are correctly written or check for possible errors in the question.