An electron is moving at 7.20 ×10^6 m / s in a magnetic field of strength 83.0 mT. What is the

step 1 In this question, we have an electron. It's moving at a speed of 7 .2 times 10 .6 meters per sec

An electron is moving at 7.20 ×10^6 m / s in a magnetic...

An electron is moving at $7.20 \times 10^{6} \mathrm{~m} / \mathrm{s}$ in a magnetic field of strength $83.0 \mathrm{mT}$. What is the (a) maximum and (b) minimum magnitude of the force acting on the electron due to the field? (c) At one point the electron has an acceleration of magnitude $4.90 \times 10^{14} \mathrm{~m} / \mathrm{s}^{2} .$ What is the angle between the electron's velocity and the magnetic field?

An electron is moving at $7.20 \times 10^{6} \mathrm{~m} / \mathrm{s}$ in a magnetic field of strength $83.0 \mathrm{mT}$. What is the (a) maximum and (b) minimum magnitude of the force acting on the electron due to the field?
(c) At one point the electron has an acceleration of magnitude $4.90 \times 10^{14} \mathrm{~m} / \mathrm{s}^{2} .$ What is the angle between the electron's velocity and the magnetic field?

Key Concepts

Centripetal Acceleration in Magnetic Fields

When a charged particle moves perpendicular to a magnetic field, the magnetic force acts as the centripetal force that causes the particle to undergo circular motion. In this context, the acceleration of the particle can be described by the centripetal acceleration formula a = v²/r, and the magnetic force provides the necessary centripetal force according to F = m a, linking the concepts of magnetic force and circular motion.

Vector Cross Product and Angle Dependence

The magnetic force on a moving charge is a result of the vector cross product between the velocity vector and the magnetic field vector. This mathematical operation implies that the force is dependent not only on the magnitudes of the velocity and magnetic field but also on the sine of the angle between them. This dependence on the angle is crucial for determining both the magnitude of the force and the conditions under which the force is maximized or minimized.

Magnetic Force on a Moving Charge

A charged particle moving in a magnetic field experiences a magnetic force described by the Lorentz force law, which is given by the equation F = qvB sin?. This force is the result of the interaction between the particle's charge and the magnetic field, and its magnitude depends on the speed of the particle, the strength of the magnetic field, and the sine of the angle between the velocity and the magnetic field directions.

Maximal and Minimal Force Conditions

The magnitude of the magnetic force is maximized when the particle’s velocity is perpendicular to the magnetic field (? = 90°), as sin90° = 1, resulting in Fmax = qvB. Conversely, the force is minimized and becomes zero when the particle's velocity is parallel or antiparallel to the magnetic field (? = 0° or ? = 180°), since sin0° = 0, meaning that no magnetic force is exerted in those cases.

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