Question

Протон движется в однородном магнитном поле с магнитной индукцией 20 мТл по окружности радиусом 5 см.Найдите скорость протона. (С ДАНО И РЕШЕНИЕМ)

Answer 1

B = 20 мТл = 0,02 Тл
R = 5 см = 0,05 м
q = 1,6*10⁻¹⁹ Кл
m = 1,67*10⁻²⁷ кг
v - ?
Fл = q*v*B*sin(α) - сила Лоренца, считаем α = 90 ° => sin(α) = 1
Fл = Fцс = m*v²/R - центростремительная сила
q*v*B = m*v²/R => v = q*R*B/m
v = 1,6*10⁻¹⁹ Кл * 0,05 м * 0,02 Тл / 1,67*10⁻²⁷ кг ≈ 9,6*10⁴ м/с = 96 км/с

Answer 2

Calculation of Proton's Velocity in a Uniform Magnetic Field

To find the velocity of a proton moving in a uniform magnetic field, we can use the formula for the centripetal force acting on a charged particle in a magnetic field:

F = qvB,

where: - F is the centripetal force, - q is the charge of the particle, - v is the velocity of the particle, and - B is the magnetic field strength.

In this case, the proton is moving in a circular path with a radius of 5 cm, so the centripetal force is provided by the magnetic force acting on the proton.

The magnetic force is given by:

F = mv² / r,

where: - m is the mass of the proton, and - r is the radius of the circular path.

Setting the two equations equal to each other, we have:

qvB = mv² / r.

Simplifying the equation, we can solve for the velocity v:

v = qBr / m.

Given: - Magnetic induction (B) = 20 mT = 20 * 10^-3 T, - Radius (r) = 5 cm = 5 * 10^-2 m, - Charge of a proton (q) = 1.6 * 10^-19 C, - Mass of a proton (m) = 1.67 * 10^-27 kg.

Substituting the values into the equation, we can calculate the velocity of the proton.

v = (1.6 * 10^-19 C) * (20 * 10^-3 T) * (5 * 10^-2 m) / (1.67 * 10^-27 kg).

Calculating the expression, we find:

v ≈ 1.91 * 10^6 m/s.

Therefore, the velocity of the proton is approximately 1.91 * 10^6 m/s.