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

pls explain how to do

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 &
F=q(v×B)
⇒F=q[Vi^×Bk^]⇒F=qVB(i^×k^)
⇒F=qvB(−j^​)
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 on the negative X direction, and
(ii) due to magnetic field
⇒F=−q(v×B)⇒F=−q[v(−i^)×B(k^)]
⇒F=qvB[i^×k^]⇒F=qvB(−j^​)
Same direction as that of positive charge.