Answer
Verified
415.2k+ views
Hint: Check whether the torque on the charge q due the force exerted by charge +Q about a point on charge +Q is zero. Note that torque is defined as the rate of change in angular momentum of the particle with respect to time.
Formula used:
$\tau =Fr$
$\tau =\dfrac{dL}{dt}$
$L=I\omega $
Complete answer:
For a particle to revolve around another particle, there must be a force attraction between the two particles. It is given that a charge q is revolving around a charge +Q in an elliptical orbit. We know that unlike charges, they attract each other. Therefore, the revolving charge q must be a negative charge.
Therefore, the +Q charge will exert a force of attraction on the charge q. The electrostatic force of attraction is always towards the charge that exerts the force. This means that the direction of the force on charge q is towards charge +Q.
The magnitude of torque on the charge about a point is equal to the product of the distance (r) between the two charges and the component of the force that is normal to r.
i.e. $\tau =Fr$.
In this case, torque about charge +Q is zero because the component of the force normal to r is zero.
i.e. $\tau =0$
And torque is defined as the rate of change in the angular momentum about the same point with respect to time.
i.e. $\tau =\dfrac{dL}{dt}$.
This means that the change in the angular momentum of charge q is zero. In other words, the angular momentum of charge q is constant.
So, the correct answer is “Option A”.
Note:
Angular momentum is given as the product of the momentum of inertia (I) and the angular velocity ($\omega $) of the particle about the same point.
i.e. $L=I\omega $.
When the charge q is moving in the elliptical path, its momentum of inertia is continuously changing because the distance of the charge q from charge Q is changing. We know that L is constant. Therefore, if I is changing then $\omega $ is also changing.
When a particle revolves in an elliptical orbit, its linear speed changes. Since the linear speed changes, the linear momentum also changes.
Formula used:
$\tau =Fr$
$\tau =\dfrac{dL}{dt}$
$L=I\omega $
Complete answer:
For a particle to revolve around another particle, there must be a force attraction between the two particles. It is given that a charge q is revolving around a charge +Q in an elliptical orbit. We know that unlike charges, they attract each other. Therefore, the revolving charge q must be a negative charge.
Therefore, the +Q charge will exert a force of attraction on the charge q. The electrostatic force of attraction is always towards the charge that exerts the force. This means that the direction of the force on charge q is towards charge +Q.
The magnitude of torque on the charge about a point is equal to the product of the distance (r) between the two charges and the component of the force that is normal to r.
i.e. $\tau =Fr$.
In this case, torque about charge +Q is zero because the component of the force normal to r is zero.
i.e. $\tau =0$
And torque is defined as the rate of change in the angular momentum about the same point with respect to time.
i.e. $\tau =\dfrac{dL}{dt}$.
This means that the change in the angular momentum of charge q is zero. In other words, the angular momentum of charge q is constant.
So, the correct answer is “Option A”.
Note:
Angular momentum is given as the product of the momentum of inertia (I) and the angular velocity ($\omega $) of the particle about the same point.
i.e. $L=I\omega $.
When the charge q is moving in the elliptical path, its momentum of inertia is continuously changing because the distance of the charge q from charge Q is changing. We know that L is constant. Therefore, if I is changing then $\omega $ is also changing.
When a particle revolves in an elliptical orbit, its linear speed changes. Since the linear speed changes, the linear momentum also changes.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Why Are Noble Gases NonReactive class 11 chemistry CBSE
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
Write a letter to the principal requesting him to grant class 10 english CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Difference Between Plant Cell and Animal Cell
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE