Question

Figure 28-28 shows the path of an electron in a region of uniform magnetic field. The path consists oftwo straight sections, each between a pair of uniformly charged plates, and two half-circles. Which plate isat the higher electric potential in

(a) the top pair of plates and

(b) the bottom pair?

(c) What is the direction of the magnetic field?

Short answer

1. Upper plate is at higher electric potential in the top pair of plates.
2. Lower plate is at higher electric potential in the bottom pair of plates.
3. Direction of magnetic field is out of the page.

Step-by-step solution

Step 1: Write the given data

Two pairs of charged plates and path of motion electrons is given in the diagram.

Determine the concept of right hand rule application

From the trajectory of electron determine which plate is at higher and which at lower potential. Then using the right hand rule, find the direction of magnetic field. According to the right-hand thumb rule, if we place our fingers in such a way that the thumb points in the direction of the magnetic field, the fore-finger points in the direction of the motion of the body, then the current flowing inside it the body due to magnetic induction points in the direction of middle finger considering that all the fingers are placed perpendicular to each other as a 3D structure.

(a) Determinewhich plate is at higher electric potential in the top pair of plates

In the given diagram, a motion of electron in anticlockwise direction is given.

When the electron enters in upper pair the charge induction will happen. And in order to keep the outside motion circular the lower plate must be at lower potential and upper plate must be at higher potential. And inside the plates in order to keep particle in straight line the electric and magnetic force must be balance each other. The electric force is upward while magnetic force is downward that is towards the center.

Hence, upper plate is at higher electric potential in the top pair of plates.

(b) Determinewhich plate is at higher electric potential in the bottom pair of plates

Similar thing as discussed in part (a), appliesto the downward pair of plates. Thus, as the electron is entering the region from left to right, the lower plate in the bottom plate of this pair is at higher potential.

Hence, lower plate is at higher electric potential in the bottom pair of plates.

(c) Determine the direction of magnetic field.

Considering a position of electron at the most left. It can be seen that the velocity is downward and magnetic force is towards the center. Then, applying right hand rule as per the concept, the direction ofas out of the page is determined.

Hence, direction of magnetic field is out of the page.