Single Choice

A deuteron of kinetic energy $$50\ keV$$ is describing a circular orbit of radius $$0.5$$ metre in a plane perpendicular to the magnetic field $$B$$. The kinetic energy of the proton that describes a circular orbit of radius $$0.5$$ metre in the same plane with the same $$B$$ is

A$$25\ keV$$
B$$50\ keV$$
C$$200\ keV$$
D$$100\ keV$$
Correct Answer

Solution

For a charged particle orbiting in a circular path in a magnetic field
$$\dfrac {mv^{2}}{r} = Bqv\Rightarrow v = \dfrac {Bqr}{m}$$
or, $$mv^{2} = Bqvr$$
Also,
$$E_{K} = \dfrac {1}{2}mv^{2} = \dfrac {1}{2}Bqvr = Bq \dfrac {r}{2}. \dfrac {Bqr}{m} = \dfrac {B^{2}q^{2}r^{2}}{2m}$$
For deuteron, $$E_{1} = \dfrac {B^{2}q^{2}r^{2}}{2\times 2m}$$
For proton, $$E_{2} = \dfrac {B^{2}q^{2}r^{2}}{2m}$$
$$\dfrac {E_{1}}{E_{2}} = \dfrac {1}{2}\Rightarrow \dfrac {50keV}{E_{2}} = \dfrac {1}{2} \Rightarrow E_{2} = 100 keV$$.

SIMILAR QUESTIONS

Magnetism

A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbits in a plane due to magnetic field perpendicular to the plane. let $$r_p$$, $$r_e$$ and $$r_{He}$$ be their respectively radii, then ,

Magnetism

A negative test charge is moving near a long straight wire carrying a current. The force acting on the test charge is parallel to the direction of the current. The motion of the charge is :

Magnetism

A positively charged particle projected towards east is deflected towards north by a magnetic field. The field may be :

Magnetism

In the x-y-plane, the region $$y > 0$$ has a uniform magnetic field $$B_1\hat{k}$$ and the region $$y < 0$$ has another uniform magnetic field $$B_2\hat{k}$$. A positively charged particle is projected from the origin along the positive $$y$$-axis with speed $$V_o = \pi ms^{-1}$$ at $$t = 0$$, as shown in the figure. Neglect gravity in this problem. Let $$t = T$$ be the time when the particle crosses the x-axis from below for the first time. If $$B_2 = 4B_1$$, the average speed of the particle, in $$ms^{-1}$$, along the x-axis in the time interval $$T$$ is ________.

Magnetism

When a positively charged particle enters into a uniform magnetic field with uniform velocity, its trajectory can be (i) A straight line (ii) A circle (iii) A helix

Magnetism

A particle is projected in a plane perpendicular to a uniform magnetic field. The area bounded by the path described by the particle is proportional to

Magnetism

An electron is moving along the positive $$X$$-axis. You want to apply a magnetic field for the short time so that the electron may reverse its direction and move parallel to the negative $$X$$-axis. This can be done by applying the magnetic field along :

Magnetism

A charged particle moves in a uniform magnetic field. The velocity of the particle at some instant makes an acute angle with the magnetic field. The path of the particle will be

Magnetism

A particle moves in a circle of diameter 1.0 cm under the action of a magnetic field of 0.40 T. An electric field of $$ 200 V m^{-1}$$ makes the path straight . Find the charge / mass ratio of the particle.

Magnetism

Which of the following particle will describe the smallest circle when projected with same velocity perpendicular to magnetic field?

Contact Details