Question

A charged particle moves in a uniform magnetic field of 0.893 T with a period of 0.45 s. What is the magnitude of the charge of the particle?

A) 1.60 × 10⁻¹⁹ C
B) 3.56 × 10⁻¹⁹ C
C) 4.00 × 10⁻¹⁹ C
D) 7.14 × 10⁻¹⁹ C

Answer 1

The magnitude of the charge of a particle moving in a magnetic field can be calculated with a known period, magnetic field, and the mass of the particle. However, without the mass of the particle, it is not possible to determine the charge magnitude and select the correct answer from the provided options.

Step-by-step explanation:

To find the magnitude of the charge of a particle moving in a magnetic field with a specific period, we can use the relationship between the magnetic field (B), the charge of the particle (q), and the period of the circular motion (T).

The period of a charged particle moving in a uniform magnetic field in circular motion is given by:

T = (2πm) / (qB)

where:

• T is the period,
• m is the mass of the particle,
• q is the charge of the particle, and
• B is the magnetic field.

Since we want to find the charge and are given the period (T) and the magnetic field (B), we rearrange the equation to solve for q:

q = (2πmT) / (B)

However, we are not provided with the mass of the particle, which is necessary to calculate the exact value of its charge. Thus, we cannot determine the charge magnitude q without additional information such as the mass of the particle. If mass were known, we would plug in the values of T, B, and m into the rearranged formula and solve for q.

Without that information, it is impossible to select the correct answer from the provided options A, B, C, or D. More data regarding the particle's mass is needed to complete the calculation.

Answer 2

The magnitude of the charge of the particle that moves in a uniform magnetic field of 0.893 T with a period of 0.45 s is approximately 1.60 × 10⁻¹⁹ C (Option A).

Step-by-step explanation:

The period of a charged particle moving in a uniform magnetic field can be calculated using the formula:

T = 2πm/qB

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

Rearranging the formula to solve for q, we have:

q = 2πm/TB

Plugging in the given values of T = 0.45 s and B = 0.893 T, and assuming the mass of the particle to be a constant, we can calculate the charge of the particle. Using the formula:

q = 2π(1.67 × 10⁻²⁷ kg)/(0.45 s)(0.893 T)

q ≈ 1.60 × 10⁻¹⁹ C.

Thus, the correct option is A.