Question

In Fig. 24-33, a particle is to be released at rest at point A and then is to be accelerated directly through point B by an electric field. The potential difference between points A and B is 100v . Which point should be at higher electric potential if the particle is (a) an electron, (b) a proton, and (c) an alpha particle (a nucleus of two protons and two neutrons)? (d) Rank the kinetic energies of the particles at point B, greatest first.

Short answer

Answer:

1. The point that should be at higher potential if the particle is an electron is B.
2. The point that should be at higher potential if the particle is an electron is A.
3. The point that should be at higher potential if the particle is an electron is A.
4. The rank of the kinetic energies of the particles at point B is

Step-by-step solution

The given data:

The potential difference between points A and B is V=100V .

Figure 24-33, shows the particle released at rest from point A and that is accelerated to point B.

Understanding the concept of potential and kinetic energy

All negative charges move from a region of lower to higher potential and the positive charges move from a region of higher to lower potential. Thus, according to the charge value, the potential can be determined. Now, the kinetic energy of a body for a given speed of the particle differs by its mass value. Thus, the higher the mass; the higher the kinetic energy of the particle

Formulae:

The electric potential at a point due to an individual charge,

$V=kq/r$ ….. (i)

The kinetic energy of the particle in motion,

K=qV ….. (ii)

Here, V is the electric potential, K is the Coulomb’s constant, q is the charge, and K is the kinetic energy.

(a) Calculation of the point of higher potential if the particle is an electron

The electron always move in direction opposite to the flow of current and a current flow from high potential to low potential. Therefore, an electron moves from lower potential to a higher potential.

For the given particle being an electron, the potential at A will be negative as the charge value becomes negative.

Hence, the point B should be at higher potential.

(b) Calculation of the point of higher potential if the particle is a proton:

A proton moves in the direction of flow of current and the current flows high potential to low potential. Therefore, a proton moves from higher to a lower potential.

For the given particle being a proton, the potential at A will be positive as the charge value becomes positive.

Hence, the point A should be at higher potential.

c) Calculation of the point of higher potential if the particle is an electron

An alpha particle is a positive partial with no electrons. Therefore, it is positive charge which has the same property as a proton. Therefore, it will also move from a higher potential to a lower potential.

For the given particle being an electron, the potential at A will be positive as the charge value becomes positive due to the presence of two protons.

Hence, point A should be at a higher potential than point B for the alpha particle.

(d) Calculation of the rank of kinetic energies of the particles:

Solve equation (i), for electron by substituting known values as below.

Solve equation (i), for proton by substituting known values as below.

Solve equation (i), for alpha by substituting known values as below.

Thus, the rank of the kinetic energy of the particles is given by:

Hence, the rank of the kinetic energies is .