A charged particle with a charge-to-mass ratio of |q|/m = 5.7 × 108 C/kg travels on a circular path that is perpendicular to a magnetic field whose magnitude is 0.86 T. How much time does it take for the particle to complete one revolution?

To find the time it takes for the charged particle to complete one revolution in a circular path, we can use the formula for the period of a charged particle in a magnetic field.

The formula for the period of a charged particle in a magnetic field is given by:

T = (2πm) / (|q|B)

where:
T is the period,
m is the mass,
|q| is the magnitude of the charge, and
B is the magnitude of the magnetic field.

In this case, we are given the charge-to-mass ratio, |q|/m, which is 5.7 × 10^8 C/kg, and the magnitude of the magnetic field, B, which is 0.86 T.

To find the time, we need to solve for T using the given values.

T = (2πm) / (|q|B)
T = (2π * 1kg) / (5.7 × 10^8 C/kg * 0.86 T)
T = (2π) / (5.7 × 10^8 * 0.86)
T ≈ 1.204 × 10^(-9) s

Therefore, it takes approximately 1.204 × 10^(-9) seconds for the charged particle to complete one revolution in the circular path.