In a certain region of space there are homogeneous

In a certain region of space, homogeneous electric and magnetic fields were discovered, the vectors E and B of which are co-directed. It is necessary to determine the acceleration a with which an electron will move if it enters these fields at a speed of V = 600 m/s at an angle of 60° to the lines of vectors E and B, if E = 0.2 kV/m, B = 20 mT.

To solve this problem, we will use Lorentz's law, which describes the motion of a particle in an electromagnetic field. According to this law, a charged particle in an electromagnetic field is acted upon by the Lorentz force and acceleration a, which can be found by the formula:

a = F / m

where F is the Lorentz force, m is the particle mass.

The Lorentz force is calculated by the formula:

F = q * (E + v x B)

where q is the charge of the particle, E is the electric field, B is the magnetic field, v is the velocity of the particle.

The vector product of speed and magnetic field can be calculated using the formula:

v x B = |v| * |B| * sin(s) * n

where α is the angle between vectors v and B, n is a unit vector perpendicular to the plane formed by vectors v and B.

In this problem, vectors E and B are co-directional, so the angle α between vectors v and B will be equal to 60°.

Now we can write the equation for particle acceleration:

a = q * (E + |v| * |B| * sin(60°) * n) / m

Let's substitute the known values:

a = 1.6 * 10^-19 Kl * (0.2 * 10^3 V/m + 600 m/s * 20 mT * sin(60°) * n) / 9.1 * 10^-31 kg

Let's express the sine of 60° through its value:

a = 1.6 * 10^-19 C * (0.2 * 10^3 V/m + 600 m/s * 20 mT * √3 / 2 * n) / 9.1 * 10^-31 kg

Considering that the unit vector n can be anything, let us represent it in the form n = (cos α, sin α, 0), where α is an arbitrary angle. Then:

a = 1.6 * 10^-19 C * (0.2 * 10^3 V/m + 600 m/s * 20 mT * √3 / 2 * sin α) / 9.1 * 10^-31 kg

The answer will be the minimum acceleration value, since the electron will move along a circular arc of radius R = |v| / |B|, and the Lorentz force will be directed towards the center of the circle. The minimum acceleration value is achieved at sin α = -1, then:

a = 1.6 * 10^-19 C * (0.2 * 10^3 V/m - 600 m/s * 20 mT * √3 / 2) / 9.1 * 10^-31 kg

a ≈ -2.69 * 10^14 m/s^2

Thus, an electron will move along a circular arc with an acceleration of -2.69 * 10^14 m/s^2 if it flies into uniform electric and magnetic fields at a speed of 600 m/s at an angle of 60° to the lines of vectors E and B, and E = 0.2 kV/m, B = 20 mT. The charge of an electron is 1.6 * 10^-19 C, and its mass is 9.1 * 10^-31 kg. To solve, Lorentz's law, the formula for the Lorentz force, and the expression for the cross product were used.

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The product contains a detailed description of a problem that involves uniform electric and magnetic fields in a certain region of space. In the problem, it is necessary to determine the acceleration of an electron flying into these fields at a certain angle, if the values ​​of the electric and magnetic fields are known.

The solution to the problem is based on the application of Lorentz's law, the formula for the Lorentz force and the expression for the vector product. All formulas and laws used in the solution are described in detail, which allows you to understand the principles of solving the problem and apply them to solve other problems in this area.

Our product is an excellent resource for students, teachers and anyone interested in physics. Beautiful design and convenient format will allow you to quickly find the necessary information and effectively use it to solve problems.

The offered product is a digital product that contains a detailed solution to a problem associated with uniform electric and magnetic fields in a certain region of space. In the problem, it is necessary to determine the acceleration of an electron flying into these fields at a speed of 600 m/s at an angle of 60° to the lines of vectors E and B, if the values ​​of the electric and magnetic fields are known (E = 0.2 kV/m, B = 20 mT) .

The solution to the problem is based on the application of Lorentz's law, the formula for the Lorentz force and the expression for the vector product. All formulas and laws used in the solution are described in detail, which allows you to understand the principles of solving the problem and apply them to solve other problems in this area.

The product is presented in html format, which makes it easy and convenient to familiarize yourself with the material and quickly find the necessary information. The beautiful design and user-friendly format make this product an excellent resource for students, teachers, and anyone interested in physics.

By purchasing this product, you receive a complete and understandable solution to the problem, which can be used for educational purposes or in preparation for exams.

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This product is a file in image format containing the solution to problem 00070, related to the movement of an electron in uniform electric and magnetic fields. The problem specifies the values ​​of the electric field E = 0.2 kV/m and the magnetic field B = 20 mT, as well as the initial velocity of the electron V = 600 m/s and the angle of its entry to the lines of vectors E and B equal to 60 degrees.

The solution to the problem includes a brief description of the condition, a listing of the formulas and laws used, the derivation of the calculation formula and the answer to the question of the problem. If you have any questions about solving the problem, the seller is ready to help.

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