Question

В однорідне магнітне поле з індукцією В=10мТл перпендикуля- рно до ліній індукції влітає електрон, кінетична енергія якого Wk = 30кеВ. Обчислити радіус кривизни траєкторії руху електронів у полі.

Answer 1

To calculate the radius of curvature of the electron's trajectory in a uniform magnetic field, we can use the formula for the centripetal force experienced by a charged particle moving in a magnetic field.

Formula:

The formula for the centripetal force is given by:

F = (m*v^2) / r

where: - F is the centripetal force - m is the mass of the electron - v is the velocity of the electron - r is the radius of curvature of the trajectory

In this case, the centripetal force is provided by the magnetic force acting on the electron:

F = q*v*B

where: - q is the charge of the electron - B is the magnetic field strength

By equating the two expressions for the centripetal force, we can solve for the radius of curvature.

Solution:

Given: - Induction of the magnetic field (B) = 10 mT = 10 * 10^-3 T - Kinetic energy of the electron (Wk) = 30 keV = 30 * 10^3 eV

To calculate the radius of curvature, we need to find the velocity of the electron. We can use the kinetic energy to find the velocity using the equation:

Wk = (1/2) * m * v^2

Solving for v:

v = sqrt((2 * Wk) / m)

The mass of an electron (m) is approximately 9.10938356 × 10^-31 kg.

Now, we can substitute the values of q, v, and B into the equation for the centripetal force:

q * v * B = (m * v^2) / r

Simplifying the equation, we get:

r = (m * v) / (q * B)

Let's calculate the radius of curvature using the given values:

- q = charge of an electron = -1.602176634 × 10^-19 C - m = mass of an electron = 9.10938356 × 10^-31 kg - B = 10 * 10^-3 T - v = sqrt((2 * 30 * 10^3 * 1.602176634 × 10^-19) / (9.10938356 × 10^-31))

Calculating the value of v, we find:

v ≈ 5.427 * 10^6 m/s

Now, substituting the values into the equation for the radius of curvature:

r = (9.10938356 × 10^-31 * 5.427 * 10^6) / (1.602176634 × 10^-19 * 10 * 10^-3)

Calculating the value of r, we find:

r ≈ 3.187 * 10^-2 m

Therefore, the radius of curvature of the electron's trajectory in the given magnetic field is approximately 3.187 * 10^-2 meters.

Please note that the calculations provided are based on the given information and assumptions.