An ionised gas contains both positive and negative ions initially at rest. If it is subjected simultaneously to an electric field along the +x-direction and a magnetic field along the +z-direction, then

Options

A. positive ions deflect towards +y direction and negative ions towards -y direction
B. all ions deflect towards +y direction
C. all ions deflect towards -y direction
D. positive ions deflect towards -y direction and negative ions towards +y direction

Answer

c

Explanation

Case of positively charged particle: Two forces are acting
on the positively charged particle (i) force due to electric
field in the positive x direction, and (ii) force due to magnetic
field.
`vecF=q(vecvxxvecB)`
`implies vecF=q[vhatixxBhatk] implies vecF=qvB(hatixxhatk)`
`implies vecF=qvB(-hatj)`
This force will deflect the positively charged particle toward
-y axis.
Case of negatively charged particle:
Two forces are acting on the negatively charged particle
(i) due to electric field in the negative X direction, and
(ii) due to magnetic field
` implies vecF=-q(vecvxxvecB) implies vecF=-q[v(-hati)xxB(hatk)] `
`implies vecF=qvB[hatixxhatk] impliesvecF=qvB(-hatj)`
Same direction as that of positive charge. (c) is the correct
answer.