Question

A proton projected with kinetic energy K describes a circle of radius r in a uniform magnetic field. With what kinetic energy should an -particle be projected in the same magnetic field so that it describes a circle of radius 2r?

Solution

Correct option is

4K

In term of kinetic energy K, the radius of the circular path is given by 

          

For -particle, the mass is 4 m and charge is 2e. Hence 

         

              

               

               = 4K.

SIMILAR QUESTIONS

Q1

An electron and a proton are projected in a uniform magnetic field with equal initial linear momenta in a direction perpendicular to the field. Then

Q2

An electron and a proton are projected in a uniform magnetic field with equal kinetic energies in a direction perpendicular to the field. Then  

Q3

A beam of electrons is projected with a velocity  in a region of crossed electric and magnetic fields E and B. If E = 800 Vm–1, the magnitude of B for electron beam to pass through the fields undeviated will be 

Q4

A proton (mass m, charge e), projected with a velocity v passes undeviated through a region of crossed electric and magnetic fields. With what velocity should an alpha-particle (mass 4 m, charge 2e) be projected so that it passes undeviated through the same region?  

Q5

Two electron beams having velocities in the ratio of 1 : 2 are subjected separately to identical magnetic fields. The ratio of deflections produced is 

Q6

A uniform magnetic field is present in the vertically downward direction in a given region. When an electron is projected in a horizontal direction to the right, it will be moving in a circular path with constant speed 

Q7

In a cathode ray tube, the electrons are subjected to a potential difference of 182 V. The maximum speed acquired by the electrons is 

Q8

Electrons are projected with a velocity of  at right angles to a magnetic field of . If the radius of the circular path of electrons is 1 cm, what is the specific charge (charge to mass ratio) of electrons?

Q9

A proton projected with a velocity v describes a circle of radius r in a uniform magnetic field. With what velocity should an alpha-particle be projected so that it describes a circle of the same radius r in the same magnetic field?   

Q10

A proton and an -particle projected with equal linear momenta describe circular paths of radii r1 and r2 respectively in a uniform magnetic field. The ratio  is