Answer
425.1k+ views
Hint: Here we see that the uniform magnetic field is perpendicular to the plane in which the two particles $A$ and $B$ of masses ${m_A}$ and ${m_B}$respectively and having the same charge are moving. When any charge particle moves perpendicular to the existing uniform magnetic field then the force which will act due to the interaction of magnetic field and charge particle will act as centripetal force and thus the particle will perform the circular motion.
Complete step by step answer:
As we know that the path of a charge particle in a uniform magnetic field is circular so the formula for the radius of the circle will be,
$r = \dfrac{{mv}}{{qB}}$, where $m = $mass of the charge particle, $v = $velocity of the charge particle, $q = $charge on the particle, $B = $external magnetic field.
Here we see that the external magnetic field and charge on the particle is the same for both the particles.
So, the mass and the velocity of the charge particles will determine the radius of the circle which is made by the motion of the particles.
From the diagram we see that the ${r_A} > {r_B}$
And mass and velocities both are directly proportional to the radius.
So, the mass of particle $A$ is more than that of the $B$.
i.e. ${m_A} > {m_B}$-----equation (2)
and the velocities will also be having the same relation as that of the mass, that means the velocity of $A$ will be more than that of the $B$.
i.e. ${v_A} > {v_B}$----equation (2)
so, on combining both the equations (equation (1) and equation (2)), we get
i.e. ${m_A}{v_A} > {m_B}{v_B}$
Hence the option (B) is the correct answer.
Note:
If we consider a general situation in which the charge particle is moving with some velocity in an external magnetic field then the force that will be acting on the particle will not perform any work on the charge particle. Therefore, the energy of a charged particle cannot be increased by the use of the magnetic field. Here in this given condition velocity and magnetic field are perpendicular to each other which makes the particle to perform the circular motion and this property is used in accelerator and fusion applications.
Complete step by step answer:
As we know that the path of a charge particle in a uniform magnetic field is circular so the formula for the radius of the circle will be,
$r = \dfrac{{mv}}{{qB}}$, where $m = $mass of the charge particle, $v = $velocity of the charge particle, $q = $charge on the particle, $B = $external magnetic field.
Here we see that the external magnetic field and charge on the particle is the same for both the particles.
So, the mass and the velocity of the charge particles will determine the radius of the circle which is made by the motion of the particles.
From the diagram we see that the ${r_A} > {r_B}$
And mass and velocities both are directly proportional to the radius.
So, the mass of particle $A$ is more than that of the $B$.
i.e. ${m_A} > {m_B}$-----equation (2)
and the velocities will also be having the same relation as that of the mass, that means the velocity of $A$ will be more than that of the $B$.
i.e. ${v_A} > {v_B}$----equation (2)
so, on combining both the equations (equation (1) and equation (2)), we get
i.e. ${m_A}{v_A} > {m_B}{v_B}$
Hence the option (B) is the correct answer.
Note:
If we consider a general situation in which the charge particle is moving with some velocity in an external magnetic field then the force that will be acting on the particle will not perform any work on the charge particle. Therefore, the energy of a charged particle cannot be increased by the use of the magnetic field. Here in this given condition velocity and magnetic field are perpendicular to each other which makes the particle to perform the circular motion and this property is used in accelerator and fusion applications.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)