Two identical point charges of 0.2 µC move in

Two point charges with the same charge of 0.2 µC move in the same plane along mutually perpendicular straight lines. The speeds of the charges are different: one charge moves at a speed of 2 mm/s, and the other at a speed of 3 mm/s. At some point in time, the charges find themselves at a distance of 10 cm from the point of intersection of their motion trajectories, moving away from it. It is necessary to determine the magnetic field induction at the point of intersection of the charge trajectories at this point in time. To solve this problem, it is necessary to use the formula for calculating the magnetic field induction created by moving point charges: Where:

• B - magnetic field induction at the point of intersection of charge trajectories
• k - electromagnetic coupling constant (9 * 10^9 N * m^2/C^2)
• q - point charge charge
• v - point charge speed
• r - distance from a point charge to the point of intersection of charge trajectories
• i - the angle between the velocity vector of a point charge and the vector connecting the point charge and the intersection point

Using this formula, you can calculate the magnetic field induction at the point of intersection of the charge trajectories at a given point in time. Our digital product is a problem on the topic of electromagnetism: “Two identical point charges of 0.2 µC move in the same plane along mutually perpendicular straight lines.” This problem is an excellent tool for applying the theory of electromagnetism in practice. The design of our product is made in a beautiful html format, which makes it easy to read and attractive to users. You can easily read the problem statement and use it for your educational purposes or for solving specific problems in the field of electromagnetism. Our product has high quality and calculation accuracy, which ensures the reliability of the results. You can be confident that the values ​​obtained will be accurate and meet the requirements of the task. By purchasing our digital product, you get access to a high-quality problem on the topic of electromagnetism with a beautiful html design, which ensures ease of use and ease of comprehension of the material. Our product is an excellent choice for students and professionals in the field of electromagnetics.

Our digital product is a problem on the topic of electromagnetism, which describes the movement of two identical point charges of 0.2 μC in the same plane along mutually perpendicular straight lines. The charge velocities differ and are equal to 2 Mm/s and 3 Mm/s. At some point in time, the charges are at a distance of 10 cm from the point of intersection of their motion trajectories, moving away from it. It is necessary to determine the magnetic field induction at the point of intersection of the charge trajectories at this point in time.

To solve this problem, it is necessary to use a formula to calculate the magnetic field induction created by moving point charges:

B = k * (q1 * v1 * sin(theta1) + q2 * v2 * sin(theta2)) / r^2

Where:

• B - magnetic field induction at the point of intersection of charge trajectories
• k - electromagnetic coupling constant (9 * 10^9 N * m^2/C^2)
• q1 and q2 - charges of point charges
• v1 and v2 - velocities of point charges
• theta1 and theta2 are the angles between the point charge velocity vector and the vector connecting the point charge and the intersection point
• r - distance from a point charge to the point of intersection of charge trajectories

By substituting known values ​​into the formula and performing calculations, we obtain the answer to the problem. Our product contains a detailed solution with a brief record of the conditions, formulas and laws used in the solution, the output of the calculation formula and the answer. The product design is made in a beautiful html format, which makes it easy to read and attractive to users.

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This product is a task of a physical level of complexity, and not a specific product. The solution to this problem can be presented as:

From the conditions of the problem it is known that two identical point charges of 0.2 μC move in the same plane along mutually perpendicular straight lines. The charge velocities are different and equal to 2 Mm/s and 3 Mm/s, respectively. At some point in time, the charges find themselves at the same distance of 10 cm from the point of intersection of their motion trajectories, moving away from this point.

It is necessary to determine at this moment in time the magnetic field induction at the point of intersection of the charge trajectories.

To solve this problem, you can use the Biot-Savart-Laplace law, which expresses the magnetic field induction at point P, caused by the flow of current I through an elementary section of the circuit with length ds and normal vector to the circuit plane dn:

d B = μ₀/4π * I * (d l × d n) / r²

where μ₀ is the magnetic constant, I is the current strength, d l is the elementary section of the circuit, d n is the normal vector to the plane of the circuit, r is the distance from the elementary section of the circuit to point P.

For this problem, the current strength I flowing through an elementary section of the circuit can be expressed in terms of the speed v of the charge and its charge q:

I = q*v

Also in this problem it is necessary to take into account the interaction of two charges with each other, which occurs by the Coulomb force:

F = (1/4πε) * (q₁*q₂) / r²

where ε is the electrical constant, q₁ and q₂ are the charges of the charges, r is the distance between the charges.

To solve the problem, we can divide the motion of charges into two components: the motion of a pair of charges as a center of mass and the motion of charges relative to the center of mass.

For a pair of charges as the center of mass, the speed of movement can be found as the arithmetic mean of the speeds of the two charges:

v = (v₁ + v₂) / 2

Next, you can find the distance from the elementary section of the circuit to the point of intersection of the charge trajectories using the Pythagorean theorem:

r = √(d² + R²)

where d is the distance from the elementary section of the circuit to the point of intersection of the charge trajectories, R is the distance between the charges.

To move charges relative to the center of mass, you can use Coulomb's law to find the force acting on each charge and then apply Newton's second law:

F = qE + qv×B, where E is the electric field, B is the magnetic field

ma = qE + q*v×B, where m is the mass of the charge, a is the acceleration of the charge.

Thus, it is possible to solve a system of equations for the motion of charges and find the magnetic field at the point of intersection of their trajectories.

A detailed solution to this problem can be found in the appropriate physics textbook or on the Internet.

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