Determine the magnetic induction of the electron field at point A

How to determine the magnetic induction of an electron's field at point A, which is located at a distance b from

Product code: MAG-001

Product name: Determination of the magnetic induction of the electron field at point A

Product description: This digital product is a solution to the problem of determining the magnetic induction of the electron field at point A. This solution is based on the known speed of the electron equal to 10^5 m/s and the distance b from the electron to point A, which makes an angle alpha with the vector electron speed. The formula for calculating the alpha angle is given as part of the solution, and it is also indicated that b = N nm, and the alpha angle = N degrees.

In addition, the product includes a solution to the problem of determining the circulation of the magnetic induction vector along a contour L, which has the shape of a circle passing through point A. The plane of the circle is perpendicular to the electron velocity vector, and the center is located on the electron trajectory.

This digital product is intended for physics students and professionals who are interested in magnetic fields and their effects on charges. The solution to the problem includes detailed calculations and step-by-step explanations, which makes the process of understanding and studying this material easier and more fun.

Product price: 199 rubles.

Note: The HTML markup of the product is made in accordance with the latest web design trends, which ensures a convenient and aesthetic presentation of product information.

This digital product is a solution to the problem of determining the magnetic induction of the electron field at point A at a distance b from it in the direction making an angle alpha with the electron velocity vector. The solution is based on the known speed of the electron, equal to 10^5 m/s, and the distance b, which makes an angle alpha with the electron speed vector. The solution contains a formula for calculating the alpha angle, and also indicates that b = N nm, and the alpha angle = N degrees.

The product also includes a solution to the problem of determining the circulation of the magnetic induction vector along a contour L, which has the shape of a circle passing through point A. The plane of the circle is perpendicular to the electron velocity vector, and the center is located on the electron trajectory.

This digital product is intended for students and professionals in the field of physics who are interested in magnetic fields and their effect on charges. The solution to the problem includes detailed calculations and step-by-step explanations, which makes the process of understanding and studying this material easier and more fun.

The price of the product is 199 rubles. The product contains HTML markup made in accordance with the latest web design trends, which provides a convenient and aesthetic presentation of information about the product. If you have any questions about solving the problem, the author of the product is ready to help.

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To solve the problem, it is necessary to use the formula for the magnetic induction of the field created by a moving charge:

B = μ₀qv sin(α) / 4πr²,

where μ₀ is the magnetic constant, q is the electron charge, v is the electron speed, r is the distance from the electron to point A, α is the angle between the electron speed vectors and the vector drawn from the electron to point A.

Let's substitute the known values:

B = (4π * 10^-7 * 1.6 * 10^-19 * 10^5 * sin(N grad)) / (4π * (N * 10^-9)^2) = 1.6 * 10^-5 * sin(N city) / N² Tl.

To determine the circulation of the magnetic induction vector along the contour L, it is necessary to calculate the value of the integral from the scalar product of the magnetic induction vector and the element of the contour length dl:

∮L B·dl.

Since the contour L is a circle, to calculate the integral you can use the formula for the length of the arc of a circle:

L = 2πR sin(θ/2),

where R is the radius of the circle, θ is the angle at which the circular arc with the center on the electron trajectory is visible.

Thus,

∮L B·dl = ∫₀²π B(R cos(φ), R sin(φ)) · (-R sin(φ) dφ, R cos(φ) dφ) = - 2πR² ∫₀²π B(R cos(φ) , R sin(φ)) sin(φ) dφ.

Let's substitute the value of B:

∮L B·dl = - 2πR² ∫₀²π (1.6 * 10^-5 * sin(N град) / N²) R sin(φ) dφ = - 3.2 * 10^-5 π R³ sin(N град) / N².

Answer: the magnetic induction of the electron field at point A is equal to 1.6 * 10^-5 * sin(N deg) / N² T, the circulation of the magnetic induction vector along the contour L is equal to - 3.2 * 10^-5 π R³ sin(N deg) / N² .

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