An electron experiences a magnetic force of magnitude 4.60 x10^-15 N when moving at an angle of 60.0° with respect to a magnetic field of magnitude 3.50 x 10^-3 T. Find the speed of the electron.

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Identify the formula for the magnetic force on a moving charge: \( F = qvB \sin(\theta) \), where \( F \) is the magnetic force, \( q \) is the charge of the electron, \( v \) is the speed of the electron, \( B \) is the magnetic field strength, and \( \theta \) is the angle between the velocity and the magnetic field.

Rearrange the formula to solve for the speed \( v \): \( v = \frac{F}{qB \sin(\theta)} \).

Substitute the known values into the equation: \( F = 4.60 \times 10^{-15} \) N, \( q = 1.60 \times 10^{-19} \) C (the charge of an electron), \( B = 3.50 \times 10^{-3} \) T, and \( \theta = 60.0^\circ \).

Calculate \( \sin(60.0^\circ) \), which is a trigonometric function value that can be found using a calculator or trigonometric table.

Substitute all the values into the rearranged formula to find \( v \): \( v = \frac{4.60 \times 10^{-15}}{1.60 \times 10^{-19} \times 3.50 \times 10^{-3} \times \sin(60.0^\circ)} \).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Magnetic Force on a Moving Charge

The magnetic force on a moving charge is given by the equation F = qvBsin(θ), where F is the force, q is the charge, v is the velocity of the charge, B is the magnetic field strength, and θ is the angle between the velocity and the magnetic field. This equation is crucial for determining the speed of the electron in the given problem.

Trigonometric Functions

Trigonometric functions, such as sine, are used to resolve components of vectors in physics. In this context, sin(θ) is used to calculate the component of the velocity that is perpendicular to the magnetic field, which is necessary for determining the magnetic force experienced by the electron.

Electron Charge

The charge of an electron is a fundamental constant, approximately -1.60x10^-19 C. Knowing this value is essential for calculating the speed of the electron, as it is a key variable in the equation for magnetic force. The negative sign indicates the electron's negative charge, but the magnitude is used in calculations involving force.