Surface of a heated negatively charged filament

A negatively charged thread is given, on which a linear charge density of 2*10^-9 C/m and a radius of 0.5 mm are specified. the electron leaves its surface at a speed of 20 m/s. It is necessary to find the speed of the electron at a distance R=2 cm from the center of the thread.

To solve this problem, we will use the law of conservation of charge and the formula for the electric field created by the thread:

dE = k*dq/R

where dE is the elementary value of the electric field created by an element of length of a thread of length dq, k is Coulomb’s constant, R is the distance from the element of length to the point at which the field is determined.

Let's find the charge dq of the element of the thread length:

dq = λ*dl

where λ is the linear charge density, dl is the elementary section of the thread length.

Then the electric field at a point located at a distance R from the center of the thread will be equal to:

E = ∫ dE = k*λ*∫dl/R = k*λ*ln(R/r)

where r – the radius of the thread.

According to the law of conservation of energy, the kinetic energy of an electron on the surface of the thread is equal to its kinetic energy at a distance R:

mv^2/2 = mv0^2/2 - e*E*R

where m is the mass of the electron, v is its speed at a distance R from the thread, v0 is its speed on the surface of the thread, e is the charge of the electron.

Thus, we find the speed of the electron at a distance R:

v = sqrt(v0^2 - 2*e*k*λ*ln(R/r)/m*R)

Substituting the known values, we get:

v ≈ 1.98*10^7 m/s

Thus, the speed of the electron at a distance of R=2 cm from the center of the negatively charged thread will be approximately equal to 1.98*10^7 m/s.

Surface of a heated negatively charged filament

This digital product is a detailed solution to problem No. 30486, which involves the surface of a heated negatively charged filament.

You will receive a brief record of the conditions, formulas and laws used in solving the problem, the derivation of the calculation formula and the answer. Also, if you have any questions regarding the solution, you can contact us for help.

This product will be useful to students attending school or university, as well as anyone interested in electrodynamics and physics in general.

By purchasing this product, you will have access to a high-quality and detailed solution to the problem, which will help you better understand the theoretical foundations and laws relating to the surface of a heated negatively charged filament.

The surface of a heated negatively charged filament is the object that is considered in problem No. 30486. To solve this problem, it is necessary to find the speed of the electron at a distance R=2 cm from the center of the thread. It is known that on the surface of a thread an electron leaves it at a speed of 20 m/s. The thread has a negative charge, a linear charge density of 2*10^-9 C/m and a radius of 0.5 mm.

To solve the problem, the law of conservation of charge and the formula for the electric field created by the thread are used. The charge of the element of thread length, as well as the electric field at a point located at a distance R from the center of the thread, are found. According to the law of conservation of energy, the kinetic energy of an electron on the surface of the thread is equal to its kinetic energy at a distance R. Using known values, you can find the speed of the electron at a distance R=2 cm from the center of the negatively charged thread, which will be approximately 1.98*10^7 m/s .

By purchasing this product, you will receive a brief record of the conditions, formulas and laws used in solving the problem, the derivation of the calculation formula and the answer. Also, if you have any questions about the solution, you can contact the seller for help. This product will be useful to students attending school or university, as well as anyone interested in electrodynamics and physics in general.

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Product description:

A negatively charged filament is proposed, which, when heated, has a surface from which an electron leaves at a speed of 20 m/s. The linear charge density of the thread is 2*10^-9 C/m, and the radius of the thread is 0.5 mm.

To solve problem 30486 it is necessary to use the laws of electrodynamics and mechanics. In particular, to determine the speed of an electron at a distance of 2 cm from the center of the thread, you can use Coulomb’s law and the law of conservation of energy.

Calculation formula for determining the speed of an electron at a distance of 2 cm from the center of the thread:

v = sqrt(2qU/m),

where q is the charge of the electron, U is the potential difference between the surface of the thread and a point at a distance of 2 cm from its center, m is the mass of the electron.

To determine the potential difference U, it is necessary to use Coulomb's law:

U = k*q/r,

where k is the Coulomb constant, q is the charge of the thread, r is the distance between the center of the thread and the point to which the potential difference must be determined.

You can also use the law of conservation of energy to calculate the potential difference and electron speed:

qU = (mv^2)/2,

where q, U and m are defined above, and v is the desired electron speed.

Answer to problem 30486:

If the distance from the center of the thread to the point where it is necessary to determine the electron speed is equal to 2 cm, the electron speed will be approximately 3.18 * 10^6 m/s.

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17. The use of a heated negatively charged filament surface can significantly improve the quality of temperature control in various processes and improve the results of scientific and engineering research.

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