A proton moving with a constant velocity passes through a region of space without any change in its velocity. If E and B represent the electric and magnetic fields respectively identify which of the following options can be true for the space.
A) $E = 0,B = 0$
B) $E = 0,B \ne 0$
C) $E \ne 0,B = 0$
D) $E \ne 0,B \ne 0$

Hint:When a charge particle moving in magnetic field then a magnetic force${F_m}$ acts on the charge particle the direction of magnetic force can be find by the Fleming's left hand rule
And we also know that when a charge particle placed in an electric field then an electric force${F_e}$stats act on it in the direction of the field on positive charge.

Step by step solution:
Let’s talk about option A
When $E = 0,B = 0$
In this condition when electric field is zero then electric force on proton will be zero
 i.e. ${F_e} = 0$
$B = 0$ So the magnetic force on moving charge also will be zero
i.e. ${F_m} = 0$
Means when both forces are zero so proton can pass space without changing their velocity
Now option B
When $E = 0$ then the electric force on the proton will be zero
i.e. ${F_e} = 0$
But when $B \ne 0$ then magnetic force may not be zero${F_m} \ne 0$
Due to magnetic force the direction of proton will be change means velocity of proton may be change
Now option C
When $E \ne 0$ then electric force ${F_e} \ne 0$
When $B = 0$ then ${F_m} = 0$
Due to electric force the velocity of proton may be change
Now option D
When $E \ne 0$ then there is an electric force ${F_e} = qE$
And when $B \ne 0$ then there is a magnetic force ${F_m} = qvB\sin \theta $
It may be possible these force are equal and opposite to each other in a particular situation so when the net force on proton will zero then velocity of proton will not change

Hence option A and option D will be correct here

Note:When a proton moving in magnetic field then magnetic force can be defined as ${F_m} = qvB\sin \theta $
Where $q \Rightarrow $ charge of moving particle for proton $ + e$
$v \Rightarrow $ Velocity of charge
$B \Rightarrow $ Magnetic field
$\theta \Rightarrow $ Is the angle between velocity and magnetic field
When a charge particle placed in electric field then electric force can be defined as ${F_e} = qE$
Where $q \Rightarrow $ charge of particle
$E \Rightarrow $ Electric field intensity