Q47 of 91 Page 230

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.

Given-
Diameter of the circle = 1.0 cm



Thus, radius of circle, r = = 0.5 × 10−2 m



Magnetic field, B = 0.40 T



Electric field, E = 200 V m−1


From the question we can confer that, the particle is moving in a circle under the action of a magnetic field.


But when an electric field is applied on the particle, it moves in a straight line.



So, we can say that the electric field is balanced by the magnetic field ie,



Magnetic force, we know, Lorentz force F is given by -



where,


q = charge on an electron


v = velocity of the electron


B=magnetic field


θ= angle between B and v






The radius of the circular path described by a particle in a magnetic field r,



where,


m is the mass of a proton


v= velocity of the particle


B = magnetic force


q= charge on the particle = C





More from this chapter

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45

Two particles, each having a mass m are placed at a separation d in a uniform magnetic filed B as shown in figure. They have opposite charges of equal magnitude q. At time t = 0, the particles are projected towards each other, each with a speed v. Suppose the Coulomb force between the charges is switched off.

(a) Find the maximum value vm of the projection speed so that the two particles do not collide.


(b) What would be the minimum and maximum separation between the particles if v = vm/2 ?


(c) At what instant will a collision occur between the particles if v = 2vm?


(d) Suppose v = 2vm and the collision between the particles is completely inelastic. Describe the motion after the collision.



 46

A uniform magnetic field of magnitude 0.20 T exists in space from east to west. With what speed should a particle of mass 0.010 g and having a charge 1.0 × 10–5 C projected from south to north so that it moves with a uniform velocity?

 48

A proton goes undeflected in a crossed electric and magnetic field (the fields are perpendicular to each other) at a speed of 2.0 × 106 ms–1. The velocity is perpendicular to both the fields. When the electric field is switched off, the proton moves along a circle of radius 4.0 cm. Find the magnitudes of the electric and the magnetic fields. Take the mass of the proton = 1.6 × 10–27 kg.

 49

A particle having a charge of 5.0 μC and a mass of 5.0 × 10–12 kg is projected with a speed of 1.0 km s–1 in a magnetic field of magnitude 5.0 mT. The angle between the magnetic field and the velocity is sin–1(0.90). Show that the path of the particle will be a helix. Find the diameter of the helix and its pitch.