Question

A charged particle moves in a uniform magnetic field of 0.825 T with a period of 7.85×10⁻⁶ s. Find its charge-to-mass ratio ||/m.

Answer 1

The charge-to-mass ratio (|q|/|m|) of the charged particle moving in the uniform magnetic field is approximately 1.09 × 10⁷ C/kg.

Step-by-step explanation:

The formula to calculate the charge-to-mass ratio (|q|/|m|) of a charged particle moving in a magnetic field is given by the equation:

`\[ (|q|)/(|m|) = (4 \pi^2)/(B^2 T), \]`

where
`\( B \)` is the magnetic field strength and
`\( T \)` is the period of the motion.

Given the magnetic field strength
`(\( B \))` as 0.825 T and the period
`(\( T \))` as 7.85 × 10⁻⁶ s, we substitute these values into the formula:

`\[ (|q|)/(|m|) = (4 \pi^2)/((0.825)^2 * 7.85 * 10^(-6)). \]`

Solving this expression yields the charge-to-mass ratio.

In summary, by applying the given values to the formula for the charge-to-mass ratio and performing the necessary calculations, we find that the charged particle has a charge-to-mass ratio of approximately 1.09 × 10⁷ C