Q. 105.0( 2 Votes )
A cubical region of space is filled with some uniform electric and magnetic fields. An electron enters the cube across one of its faces with velocity v and a positron enters via opposite face with velocity - v. At this instant,
A. the electric forces on both the particles cause identical accelerations.
B. the magnetic forces on both the particles cause equal accelerations.
C. both particles gain or lose energy at the same rate.
D. the motion of the center of mass (CM) is determined by B alone.
Force on a moving charged particle due to uniform magnetic field is given by qv×B where,
q is charge of particle;
v is velocity vector with which charged particle is moving in the magnetic field;
B is magnetic field vector.
So, for electron magnetic force is F1= (-e)v×B = -(ev×B) and for positron magnetic force is F2= e(-v)×B = -(ev×B)
We can see that F1= F2 …(i). Magnetic force is only responsible for rotation of the charges.
Now, force on the charged particle due to electric field is given by qE where,
q is charge of the particle;
E is electric field strength.
So, for electron electric force is f1= -eE and for positron electric force is f2= eE
We can see that f1= -f2 …(ii)
(a) Due to electric force the charges experience opposite force due to their opposite charge. So, it is not the correction option.
(b) From equation (i) we can say that both experience same force and since they have equal mass so the force causes equal acceleration. So, it is correct option.
(c) Magnetic force has no role in energy gain or loss of the charges as it can do no work and only change the direction of moving charges. So, only electric field is responsible for gain or loss of the charges and since the given charges experience force of equal magnitude so the charges will gain or lose energy at same rate. So, it is correct option.
(d) The center of mass of the charges experience no force due to electric field as both the charges experience opposite force (as in equation (ii)). And, net magnetic force on the pair of charges is -2evB (on adding F �1 and F2) which will determine the motion of center of mass of the charges.
Hence our answers are option (b), (c) and (d).
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