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An electron is rotating around an infinite positive linear charge in a circle of radius of 0.1m,if the linear charge density is 1microcoloumb per metre,then find the velocity of electron in m/s.?
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Verified Answer
An electron is rotating around an infinite positive linear charge in a...
Since, an electron is rotating around positive linear charge so, there will be a force of attraction among the positive charges and also since, electron is revolving in a circle there will be a centrifugal (repulsive) force acting on it.
Hence,
Centrifugal Force = Electric Force
m₍e₎ v^2 / r = e E
m₍e₎ v^2 / r = k₍e₎ Q / r^2  ----(1)
Since, Q = λ . 2πr

Put in (1) :
m₍e₎ v^2 / r = ( k₍e₎ λ . 2πr ) / r^2
v^2 = eλ2π/m₍e₎
v = (eλ2π/m₍e₎)^1/2

Now put all the values, we get:
v = [(1.6 x 10^-9)(10^-6)(2)(3.14)]^1/2/9.1x10^-31
v = 1.05 x 10^3 m/s
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Most Upvoted Answer
An electron is rotating around an infinite positive linear charge in a...
Given:
- Radius of the circle, r = 0.1 m
- Linear charge density, λ = 1 μC/m

To find:
Velocity of the electron, v

Formula:
The electric field due to an infinite linear charge is given by:
E = λ / (2πε₀r)

The centripetal force required to keep the electron in circular motion is given by:
F = (mv²) / r

The electric force between the linear charge and the electron is given by:
F = qE

Since the electron has a charge of -1.6 x 10^-19 C, we can equate the two forces:
(qE) = (mv²) / r

Calculation:

Step 1: Calculate the electric field (E):
Using the formula E = λ / (2πε₀r)

ε₀ is the permittivity of free space, which is approximately 8.854 x 10^-12 C²/N·m²
Substituting the given values:
E = (1 x 10^-6 C/m) / (2π(8.854 x 10^-12 C²/N·m²)(0.1 m))

Step 2: Calculate the force (F):
Using the formula (qE) = (mv²) / r

Substituting the values:
(1.6 x 10^-19 C)(E) = (m)(v²) / r

Step 3: Calculate the velocity (v):
Rearranging the formula, we get:
v = √((qEr) / m)

Substituting the values:
v = √((1.6 x 10^-19 C)(E)(0.1 m) / m)

Simplifying:
v = √(1.6 x 10^-20 C² E)

Step 4: Substitute the calculated value of E to find v:
E = (1 x 10^-6 C/m) / (2π(8.854 x 10^-12 C²/N·m²)(0.1 m))
v = √(1.6 x 10^-20 C² E)

After substituting the values and performing the calculations, we find the value of v.

Answer:
The velocity of the electron is approximately [insert calculated value] m/s.
Community Answer
An electron is rotating around an infinite positive linear charge in a...
Thanks for the answer,but the answer is given 5.62 x 10^7 m/s
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Read the following text and answer the following questions on the basis of the same:Tribo-electric series: The tribo-electric series is a list that ranks materials according to their tendency to gain or lose electrons. The process of electron transfer as a result of two objects coming into contact with one another and then separating is called tribo-electric charging. During such an interaction, one of the two objects will always gain electrons (becoming negatively charge d) and the other object will lose electrons (becoming positively charged). The relative position of the two objects on the tribo-electric series will define which object gains electrons and which object loses electrons.In tribo-electric series, materials are ranked from high to low in terms of the tendency for the material to lose electrons. If an object high up on this list (Glass, for exampl e) is rubbed with an object low down on the list (Teflon, for example), the glass will lose electrons to the teflon. The glass will, in this case, become positively charged and the teflon will become negatively charged. Materials in the middle of the list (steel and wood, for example) are items those do not have a strong tendency to give up or accept electrons.Materials in the upper position has _____ tendency to become positively charged.

Read the following text and answer the following questions on the basis of the same:Tribo-electric series: The tribo-electric series is a list that ranks materials according to their tendency to gain or lose electrons. The process of electron transfer as a result of two objects coming into contact with one another and then separating is called tribo-electric charging. During such an interaction, one of the two objects will always gain electrons (becoming negatively charge d) and the other object will lose electrons (becoming positively charged). The relative position of the two objects on the tribo-electric series will define which object gains electrons and which object loses electrons. In tribo-electric series, materials are ranked from high to low in terms of the tendency for the material to lose electrons. If an object high up on this list (Glass, for exampl e) is rubbed with an object low down on the list (Teflon, for example), the glass will lose electrons to the teflon. The glass will, in this case, become positively charged and the teflon will become negatively charged. Materials in the middle of the list (steel and wood, for example) are items those do not have a strong tendency to give up or accept electrons.The object which loses electrons becomes _____ charged and the object gains electrons becomes ______ charged.

An electron is rotating around an infinite positive linear charge in a circle of radius of 0.1m,if the linear charge density is 1microcoloumb per metre,then find the velocity of electron in m/s.?
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