an electron revolves 6*10^15 time per second in a circular orbit the curren in the loop is

To determine the current in a circular loop created by an electron revolving at a frequency of \(6 \times 10^{15}\) revolutions per second, we can use the relationship between current, charge, and time. Current (\(I\)) is defined as the charge (\(Q\)) that flows through a circuit per unit time (\(t\)). The formula for current can be expressed as:

Understanding Current Calculation

The formula for current is:

I = Q / t

In this case, the electron is completing a certain number of revolutions per second, which gives us the time period for one complete revolution. The charge of a single electron is approximately \(1.6 \times 10^{-19}\) coulombs.

Step-by-Step Calculation

• Determine the time period: The time period (\(T\)) for one revolution can be calculated as the reciprocal of the frequency (\(f\)). Since the frequency is given as \(6 \times 10^{15}\) Hz, we find:

T = 1 / f = 1 / (6 \times 10^{15}) = 1.67 \times 10^{-16} seconds

• Calculate the current: Since one electron completes one revolution in this time period, the charge that passes through a point in the circuit during this time is the charge of one electron. Thus, we can substitute into the current formula:

I = Q / T = (1.6 \times 10^{-19} C) / (1.67 \times 10^{-16} s)

• Perform the calculation: Now, we can compute the current:

I ≈ 9.58 \times 10^{-3} A

Final Result

The current in the loop, as a result of the electron revolving at a frequency of \(6 \times 10^{15}\) times per second, is approximately \(9.58 \times 10^{-3}\) amperes, or 9.58 milliamperes. This illustrates how even a single electron can create a measurable current when it moves in a circular path at such high frequencies.

Real-World Application

This concept is fundamental in understanding how electric currents work in various applications, such as in the operation of electronic devices where the movement of electrons creates electrical signals. The principles behind this calculation are also applicable in fields like electromagnetism and quantum mechanics, where the behavior of particles at high speeds is crucial.