A charged particle with a charge-to-mass ratio of |q|/m = 5.7 x 10^8 C/kg travels on a circular path that is perpendicular to a magnetic field whose magnitude is 0.69 T. How much time does it take for the particle to complete one revolution?

Question

A charged particle with a charge-to-mass ratio of |q|/m = 5.7 x 10^8 C/kg travels on a circular path that is perpendicular to a magnetic field whose magnitude is 0.69 T. How much time does it take for the particle to complete one revolution?

Answer 1

ma=F

mv²/R =qvBsinα.

v⊥B => sinα = 1.
mv/R =qB,
R = mv/ qB,

T=2πR/v=2π m /qB=
= 2π/B(q/m) =2π/0.69•5.7•10⁸0.69= =1.6•10⁻⁸ s

Answer 2

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

T = 2πm / (|q|B)

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

In this case, we are given the charge-to-mass ratio (|q|/m) as 5.7 x 10^8 C/kg and the magnetic field (B) as 0.69 T. We need to find the period (T).

First, let's rearrange the formula:

T = 2πm / (|q|B)

Now, substitute the given values:

T = 2π(1 kg) / ((5.7 x 10^8 C/kg)(0.69 T))

Simplifying:

T = (2π kg) / ((5.7 x 10^8 C)(0.69))

T = (2π kg) / (3.933 x 10^8 C)

Finally, calculate the value of T:

T ≈ 1.009 x 10^-8 seconds

Therefore, it takes approximately 1.009 x 10^-8 seconds for the charged particle to complete one revolution.

Answer 3

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

T = (2π * m) / (|q| * B)

where:
T = period (time for one revolution)
m = mass of the particle
|q| = magnitude of the charge
B = magnitude of the magnetic field

Given:
|q|/m = 5.7 x 10^8 C/kg
B = 0.69 T

Let's substitute these values into the formula and solve for T:

T = (2π * m) / (|q| * B)
T = (2π * (m/kg)) / (5.7 x 10^8 C/kg * 0.69 T)
T = (2π * (m/kg)) / (3.933 x 10^8 C/(kg * T))

Now, we need to convert the units of C/(kg * T) to C/kg. Since C/(kg * T) is equivalent to N/(A * m), and 1 T = 1 N/(A * m), we can write:

T = (2π * (m/kg)) / (3.933 x 10^8 C/(kg * T)) * (1 T / 1 N/(A * m))
T = (2π * (m/kg)) / (3.933 x 10^8 C/kg)

Now, let's substitute the value of |q|/m into the equation:

T = (2π * (1kg)) / (3.933 x 10^8 C/kg)
T = (2π) / (3.933 x 10^8)

Using the given value of π as 3.14159, we can calculate T:

T = (2 * 3.14159) / (3.933 x 10^8)
T ≈ 1.006 x 10^-8 seconds

Therefore, it takes approximately 1.006 x 10^-8 seconds for the particle to complete one revolution.