Question

Как изменится кинетическая энергия заряженной частицы, если радиус окружности, по которой движется эта частица в однородном магнитном поле, уменьшается в 2 раза?

Answer 1

Сила Лоренца - центростремительная сила.

qvB = mv^2/R

Отсюда скорость частицы:

v = qBR/m

Кинетическая энергия частицы:

W = mv^2/2.

Подставив выражение для скорости, получим:

$W\ =\ \frac{q^2B^2R^2}{2m}.$

Из полученной формулы видим, что кинетическая энергия пропорциональна квадрату радиуса. Значит при уменьшении радиуса траектории в 2 раза, кинет. энергия частицы уменьшится в 4 раза.

Ответ: уменьшится в 4 раза.

Answer 2

Calculating Change in Kinetic Energy of a Charged Particle in a Magnetic Field

When the radius of the circular path along which a charged particle moves in a uniform magnetic field decreases, the kinetic energy of the particle changes. This change can be calculated using the formula for the force experienced by a charged particle in a magnetic field and the work-energy principle.

The force experienced by a charged particle moving in a magnetic field is given by the formula: F = B * q * v * sin(θ) Where: - F is the force - B is the magnetic field strength - q is the charge of the particle - v is the velocity of the particle - θ is the angle between the velocity vector and the magnetic field vector

The work done on the particle as it moves in a circular path can be calculated using the formula: W = F * d Where: - W is the work done - F is the force - d is the displacement

The change in kinetic energy can then be calculated using the work-energy principle: ΔKE = W

Calculation of Change in Kinetic Energy

When the radius of the circular path decreases, the displacement d also decreases. As a result, the work done W and the change in kinetic energy ΔKE will also change. The exact calculation of the change in kinetic energy requires the specific values of the magnetic field strength, charge of the particle, initial velocity, and the angle between the velocity vector and the magnetic field vector.

The change in kinetic energy can be calculated using the given formulas and the specific values of the parameters involved in the motion of the charged particle in the magnetic field.

Conclusion

The change in kinetic energy of a charged particle when the radius of the circular path decreases in a uniform magnetic field can be calculated using the force experienced by the particle in the magnetic field and the work-energy principle. The specific calculation requires the values of the magnetic field strength, charge of the particle, initial velocity, and the angle between the velocity vector and the magnetic field vector.