Question

In Fig. 22-29, an electron e travels through a small hole in plate A and then toward plate B. A uniform electric field in the region between the plates then slows the electron without deflecting it. (a) What is the direction of the field? (b) Four other particles similarly travel through small holes in either plate Aor plate Band then into the region between the plates. Three have charges$\mathbf{+}{\mathit{q}}_{\mathbf{1}}$
,$\mathbf{+}{\mathit{q}}_{\mathbf{2}}$
, and.$\mathbf{-}{\mathit{q}}_{\mathbf{3}}$The fourth (labeled n) is a neutron, which is electrically neutral. Does the speed of each of those four other particles increase, decrease, or remain the same in the region between the plates?

Short answer

a) The direction of the field will be from A to B.

b) For particles$+q_1\text{and\hspace{0.17em}\hspace{0.17em}}-q_3$, the speed will increase while for particle$+q_2$ will decrease and for neutron will remain same.

Step-by-step solution

Understanding the concept of deflection

The direction of the electric field is the same as that of the force on a positive charge. a force always acts on the negative charge in the direction opposite to that of the electric field.The velocity of a positive charge will increase when it moves in the same direction as the electric field and will decrease when in opposite direction to that of the electric field applied in the region. Now, if the negative charge moving in the same direction as the electric field will decelerate or vice-versa.

a) Calculation of the direction of the electric field

As the problem states, there is no deflection in the movement of the electron, and is only slowed down, thus the direction of force acting on it will be anti-parallel to its motion as per the concept. Due to this negative charge, the direction of the electric field must be along the motion of the electron as the direction of force must be opposite to the field direction.

Hence, the direction of the electric field will be from A to B.

b) Calculation of the speed of the other particles entering the region

For first particle$+q_1$,

As it is entering from hole A, it will in the direction of electric field thus will experience a force in the same direction as the field. Thus, its velocity will increase due to acceleration.

For second particle,$+q_2$

As it is entering from hole B, it will in the opposite direction of electric field thus will experience a force in the opposite direction as the field. Thus, its velocity will decrease due to acceleration.

For third particle$-q_3$,

As it is entering from hole B, being negatively charged it will in the opposite direction of electric field thus will experience a force in the opposite direction as the field. Thus, its velocity will increase due to acceleration.

For the fourth particle that is a neutron being electrically neutral will not undergo any deflection, thus, its experienced force will be zero and thus, the speed of the particle within the region will remain same.

Hence, for particles, $+q_1\text{and\hspace{0.17em}\hspace{0.17em}}-q_3$the speed will increase while for particle$+q_2$ will decrease and for neutron will remain same.