A thin endless dielectric rod is bent under

In this problem, there is a thin endless dielectric rod that is bent at an angle of 90°. One side of the corner is charged with a positive charge with linear density r = 1 nC/m, and the other side is charged with a negative charge with the same linear density. It is necessary to determine the electric field strength at a point that is located on the bisector of the angle at a distance b = 10 cm from its vertex.

We use Coulomb's law to find the magnitude of the electric field strength. To do this, we divide the rod into infinitesimal charged elements and integrate along the entire length of the rod.

Let the distance from the charge to the point at which you want to find the electric field strength be equal to r. Then, according to Coulomb’s law, the electric field strength at a given point will be equal to:

E = k * (dq / r^2) * cos(a / 2)

where k is the Coulomb constant, dq is the elementary charge, r is the distance from the elementary charge to the point at which the desired intensity is located, and is the angle between the bisector of the angle and the continuation of the adjacent side.

Let's integrate this expression for the entire rod:

E = k * r * (λ / 2π) * ∫(0→π/2) (sinθ / r^2) * cos(θ/2) dθ

where λ is the linear charge density on the rod, θ is the angle between the elementary charge and the extension of the adjacent side.

The integral can be calculated to obtain:

E = k * λ * (1 / π) * ln((1 + √2) / (1 - √2))

Substituting the known values, we get:

E = 9 * 10^9 * 1 * (1 / π) * ln((1 + √2) / (1 - √2)) N/C ≈ 2.06 * 10^5 N/C

Thus, the desired electric field strength at a point located on the bisector of the angle at a distance b=10 cm from its vertex is approximately 2.06 * 10^5 N/C.

Product description:

A thin endless dielectric rod is bent at an angle of 90°.

This product is a digital product that is designed to solve problems in the field of electrodynamics. It contains a detailed solution to the problem, which describes a situation in which one side of the corner is charged with a positive charge and the other with a negative charge, with a linear density of r = 1 nC/m.

This product provides a brief statement of the problem, formulas and laws used in the solution, the derivation of the calculation formula and the answer. If you have any questions regarding the solution, you can always contact us.

This product is a digital solution to a problem in the field of electrodynamics. It contains a detailed description of the problem conditions, formulas and laws used in the solution, the derivation of the calculation formula and the answer.

Specifically, the task is to determine the electric field strength at a point that is located on the bisector of an angle at a distance b = 10 cm from its vertex, provided that a thin infinite dielectric rod is bent at an angle of 90°, and one side of the angle is charged with a positive charge with a linear density r=1nC/m, and the other with a negative charge with the same linear density.

This product provides a brief statement of the problem, formulas and laws used in the solution, the derivation of the calculation formula and the answer.

Using Coulomb's law to find the magnitude of the electric field strength, the solution breaks the rod into infinitesimal charged elements and integrates along the entire length of the rod. The result is a formula for calculating the desired electric field strength at a given point, which is approximately 2.06 * 10^5 N/C.

If any questions arise regarding the solution, the buyer can contact the seller.

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This is a thin endless dielectric rod that is bent at an angle of 90°. One of the sides of the angle is charged with a positive charge with a linear density r = 1 nC/m, and the other side is charged with a negative charge with the same linear density.

For this product, problem 31009 was solved, where it was required to determine the electric field strength at a point located on the bisector of an angle at a distance b = 10 cm from its vertex. The problem was solved using the appropriate formulas and laws of electrostatics. As a result, a calculation formula and an answer to the problem were obtained. If you have any questions about solving the problem, I am ready to help.

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