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 (1011) 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.)

0.016

I=q/t

q=Ne
t=2πR/v
I=Nev/2πR=
=10¹¹•1.6•10⁻¹⁹•3•10⁸/2π•300 =
=0.0025 A

To determine the electric current due to the flow of electrons in the synchrotron, we need to find the total charge passing through a specific point in the circuit per unit time.

The electric current (I) is given by the formula:

I = (Q * v) / t

where Q is the charge passing through the circuit, v is the velocity of the charges, and t is the time taken for the charge to pass through the circuit.

In this case, each electron carries a charge of e = 1.6 × 10^(-19) C. The synchrotron has 100 billion electrons, so the total charge passing through the circuit is:

Q = (1.6 × 10^(-19) C/electron) * (1 × 10^11 electrons) = 1.6 × 10^(-8) C

The time taken for the electrons to complete one full orbit (T) can be calculated using the formula:

T = L / v

where L is the circumference of the circular orbit and v is the velocity of the electrons.

Substituting the given values:

T = 300 m / (3 × 10^8 m/s) = 1 × 10^(-6) s

Now, substitute the calculated values of Q and T into the formula for electric current:

I = (Q * v) / t
= (1.6 × 10^(-8) C) / (1 × 10^(-6) s)
= 16 A

Therefore, the electric current due to the flow of electrons in the synchrotron is 16 Amperes.