Question

протон с энергией 1,0 МэВ влетел в однородное магнитное поле ,перпендикулярное линям магнитной индукции. какой должна быть минимальная протяженность поля в направлении движения протона , чтобы направление его движения изменилось на противоположное ?( магнитная индукция поля В=1 Тл)

Answer 1

Дано

W=1МэВ=1,6*10^-13 Дж

В=1Тл

m=1,67*10^-27 Кг

q= 1,6*10^-19Кл 

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d – ?  

 

РЕШЕНИЕ

Протон будет вращаться в магнитном поле по окружности.

Минимальная протяженность поля d в направлении движения протона

будет равна радиусу окружности r.

r=m/q *v/B

Скорость протона найдем из формулы энергии 

W=mv^2/2

v=√(2W/m)

r= 1/(qB)* √(2Wm)=1/(1,6*10^-19*1)*√(2*1,6*10^-13*1,67*10^-27)= 14 см

Ответ Минимальная протяженность поля =14 см

Answer 2

Calculation of the Minimum Length of the Magnetic Field

To determine the minimum length of the magnetic field required to change the direction of the proton's motion, we can use the formula for the magnetic force on a charged particle moving through a magnetic field.

The formula for the magnetic force is given by:

F = qvB sin(θ)

Where: - F is the magnetic force - q is the charge of the particle - v is the velocity of the particle - B is the magnetic field strength - θ is the angle between the velocity vector and the magnetic field vector

In this case, the proton has a charge of +e (elementary charge) and an energy of 1.0 MeV. We can use the energy of the proton to calculate its velocity using the relativistic energy-momentum equation:

E = γmc^2

Where: - E is the energy of the particle - γ is the Lorentz factor (γ = 1 / sqrt(1 - (v^2 / c^2))) - m is the rest mass of the particle - c is the speed of light

Given that the energy of the proton is 1.0 MeV and the rest mass of the proton is approximately 938 MeV/c^2, we can calculate the velocity of the proton.

Let's calculate the velocity of the proton first:

E = γmc^2 1.0 MeV = γ * 938 MeV/c^2 * c^2

Simplifying the equation:

1.0 = γ * 938

Solving for γ:

γ = 1.0 / 938

Using this value of γ, we can calculate the velocity of the proton:

v = c * sqrt(1 - (1 / γ^2))

Now that we have the velocity of the proton, we can calculate the minimum length of the magnetic field required to change the direction of its motion.

The magnetic force on the proton is given by:

F = qvB sin(θ)

Since the proton's velocity is perpendicular to the magnetic field lines, the angle θ is 90 degrees, and sin(θ) = 1.

Therefore, the magnetic force simplifies to:

F = qvB

To change the direction of the proton's motion, the magnetic force must be equal to the centripetal force required to keep the proton in a circular path.

The centripetal force is given by:

F = mv^2 / r

Where: - m is the mass of the proton - v is the velocity of the proton - r is the radius of the circular path

Setting the magnetic force equal to the centripetal force:

qvB = mv^2 / r

Simplifying the equation:

r = mv / (qB)

Now we can substitute the values for the mass of the proton (approximately 1.67 x 10^-27 kg), the velocity of the proton, the charge of the proton (elementary charge), and the magnetic field strength (1 T) to calculate the minimum length of the magnetic field.

Let's calculate the minimum length of the magnetic field:

r = (1.67 x 10^-27 kg) * v / (1.6 x 10^-19 C * 1 T)

Using the calculated velocity of the proton, we can substitute the values and calculate the minimum length of the magnetic field.

Please wait a moment while I perform the calculation.