Question

Figure 28-26 shows crossed uniform electric and magnetic fields $\underset{F}{\to }$and $\underset{B}{\to }$, at a certain instant, the velocity vectors of the 10 charged particles listed in Table 28-3. (The vectors are not drawn to scale.) The speeds given in the table are either less than or greater than (see Question 5). Which particles will move out of the page toward you after the instant shown in Fig. 28-26?

Short answer

Particles 2, 5, 6,9,10 will come out of the page.

Step-by-step solution

Write the given data

Different orientation of velocity of the particles is given in the diagram and the speeds given in the table are either less than or greater than$\frac{E}{B}$.

Determining the concept

According to the right-hand thumb rule, place 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.Using the given conditions and the right hand rule, find the direction of net force acting on the particles which will give the direction of their motion.

Determine which particles will move out of the page

For particle 1:

As per the given data in the table, we can get the value of electric field as:

$\begin{array}{l}v<\frac{E}{B}\\ E>vB\end{array}$

Electric field is greater than the product of velocity and magnetic field. Hence, electric force will dominate. Since electric force is directed into the page (in the given figure), the particle will move into the page.

For particle 2:

As per the given data in the table, we can get the value of electric field as:

$\begin{array}{l}v>\frac{E}{B}\\ B>\frac{E}{v}\end{array}$

Magnetic field is greater. Hence, magnetic force will dominate. The net force on it will act in the outward direction as magnetic force is directed outward according to the right hand rule.

Hence, the particle will come out of the page.

For particle 3:

As per the given data in the table, we can get the value of electric field as:

$\begin{array}{l}v<\frac{E}{B}\\ E>vB\end{array}$

Electric field is greater than the product of velocity and magnetic field. Hence, electric force will dominate. Since particle 3 is positive, the force on it is into the page.

So, the particle will go into the page.

For particle 4:

As per the given data in the table, we can get the value of magnetic field as:

$\begin{array}{l}v>\frac{E}{B}\\ B>\frac{E}{v}\end{array}$

The velocity of the particle is downward and magnetic field is towards the left. Force acting on the particle is magnetic force, using the right hand rule, the direction of the magnetic force is into the page, electric force is also directed into the page.

Hence, the particle goes into the page.

For particle 5:

As per the given data in the table, we can get the value of electric field as:

Electric field is greater than the product of velocity and magnetic field. Hence, electric force will dominate. Since particle 5 is negative, the magnetic and electric forces on it are directed out of the page.

Hence, particle will go out of the page.

For particle 6:

As per the given data in the table, we can get the value of magnetic field as:

The velocity of particle is downward and magnetic field is towards the left. The magnetic and electric forces on it are directed out of the page.

Hence, particle will go out of the page.

For particle 7:

As per the given in the figure, the motion of the particle is parallel to the direction of the magnetic field.

There is no magnetic force acting on the particle. Since the electric force points into the page, the particle will go into the page.

For particle 8:

As per the given in the figure, the motion of the particle is parallel to the direction of the magnetic field.

Thus, there is no magnetic force acting on the particle. Since the electric force points into the page, the particle will go into the page.

For particle 9, 10:

As per the given in the figure, the motion of the particle is anti-parallel to the direction of the magnetic field.

Thus, there is no magnetic force acting on the particle. Since the electric force points out of the page, the particle will go out of the page.

Hence, particles 2, 5, 6,9,10 will come out of the page.