In a synchrotron, electrons are accelerated to speeds close to the speed of light v≈c≈3×108 m/s Suppose that in a synchrotron, 100 billion (10^11) electrons move in a circular orbit of circumference L=300 m . Determine the electric current in Amps due the flow of electrons in the synchrotron. You may assume that the electrons are homogeneously distributed over the circular orbit.
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brilliant qn (as usual) Hint: I=ceN/L
To determine the electric current due to the flow of electrons in the synchrotron, you can use the formula for electric current:
I = n*q*v
Where:
- I is the electric current in Amps,
- n is the number density of electrons,
- q is the charge of each electron, and
- v is the velocity of the electrons.
First, let's find the number density of electrons (n). Since the electrons are homogeneously distributed over the circular orbit, the number density is simply the number of electrons (N) divided by the circumference of the orbit (L):
n = N / L
Now, substitute the given values:
N = 10^11 (100 billion electrons)
L = 300 m (circumference of the orbit)
n = 10^11 / 300
After evaluating this expression, you will get the number density of electrons (n).
Next, let's determine the charge of each electron (q). The charge of an electron is approximately -1.6 x 10^-19 Coulombs.
q = -1.6 x 10^-19 C
Finally, substitute the values of n, q, and the velocity of the electrons (v) into the formula for electric current:
I = n*q*v
v = c = 3 x 10^8 m/s (velocity of the electrons)
I = (10^11 / 300) * (-1.6 x 10^-19 C) * (3 x 10^8 m/s)
After evaluating this expression, you will get the electric current (I) in Amps due to the flow of electrons in the synchrotron.