###### Advertisements

###### Advertisements

A particle of mass m and charge (−q) enters the region between the two charged plates initially moving along x-axis with speed v_{x} (like particle 1 in the fig.). The length of plate is L and an uniform electric field E is maintained between the plates. Show that the vertical deflection of the particle at the far edge of the plate is qEL^{2}/(2m`"v"_"x"^2`).

###### Advertisements

#### Solution

Charge on a particle of mass m = − q

Velocity of the particle = v_{x}

Length of the plates = L

Magnitude of the uniform electric field between the plates = E

Mechanical force, F = Mass (m) × Acceleration (a)

`"a" = "F"/"m"`

However, electric force, F = qE

Therefore, acceleration, `"a" = ("qE")/"m"` ......(1)

Time taken by the particle to cross the field of length L is given by,

t = `"lenght of the plate"/"Velocity of the particle" = "L"/"v"_"x"` .......(2)

In the vertical direction, initial velocity, u = 0

According to the third equation of motion, vertical deflection s of the particle can be obtained as,

`"s" = "ut" + 1/2"at"^2`

`"s" = 0 + 1/2("qE"/"m")("L"/"v"_"x")^2`

`"s" = ("qEL"^2)/(2"m""v"_"x"^2)` ........(3)

Hence, the vertical deflection of the particle at the far edge of the plate is qEL^{2}/(2m`"v"_"x"^2`).

This is similar to the motion of horizontal projectiles under gravity.

#### APPEARS IN

#### RELATED QUESTIONS

The electrostatic force on a small sphere of charge 0.4 μC due to another small sphere of charge − 0.8 μC in air is 0.2 N.

(a) What is the distance between the two spheres?

(b) What is the force on the second sphere due to the first?

Check that the ratio ke^{2}/G m_{e}m_{p}_{ }is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?

Suppose that the particle is an electron projected with velocity v_{x }= 2.0 × 10^{6} m s^{−1}. If E between the plates separated by 0.5 cm is 9.1 × 10^{2} N/C, where will the electron strike the upper plate? (|e| = 1.6 × 10^{−19} C, m_{e }= 9.1 × 10^{−31 }kg)

Find the electric force between two protons separated by a distance of 1 fermi (1 fermi = 10^{−15} m). The protons in a nucleus remain at a separation of this order.

Suppose the second charge in the previous problem is −1.0 × 10^{−}^{6} C. Locate the position where a third charge will not experience a net force.

Two charged particles are placed 1.0 cm apart. What is the minimum possible magnitude of the electric force acting on each charge?

Estimate the number of electrons in 100 g of water. How much is the total negative charge on these electrons?

Suppose all the electrons of 100 g water are lumped together to form a negatively-charged particle and all the nuclei are lumped together to form a positively-charged particle. If these two particles are placed 10.0 cm away from each other, find the force of attraction between them. Compare it with your weight.

NaCl molecule is bound due to the electric force between the sodium and the chlorine ions when one electron of sodium is transferred to chlorine. Taking the separation between the ions to be 2.75 × 10^{−8} cm, find the force of attraction between them. State the assumptions (if any) that you have made.

Suppose an attractive nuclear force acts between two protons which may be written as F=Ce^{−kr}/r^{2}. Suppose that k = 1 fermi^{−1} and that the repulsive electric force between the protons is just balanced by the attractive nuclear force when the separation is 5 fermi. Find the value of C.

Two charged particles with charge 2.0 × 10^{−8} C each are joined by an insulating string of length 1 m and the system is kept on a smooth horizontal table. Find the tension in the string.

Two identical balls, each with a charge of 2.00 × 10−7 C and a mass of 100 g, are suspended from a common point by two insulating strings, each 50 cm long. The balls are held at a separation 5.0 cm apart and then released. Find.

(a) the electric force on one of the charged balls

(b) the components of the resultant force on it along and perpendicular to the string

(c) the tension in the string

(d) the acceleration of one of the balls. Answers are to be obtained only for the instant just after the release.

Two small spheres, each with a mass of 20 g, are suspended from a common point by two insulating strings of length 40 cm each. The spheres are identically charged and the separation between the balls at equilibrium is found to be 4 cm. Find the charge on each sphere.

Two identically-charged particles are fastened to the two ends of a spring of spring constant 100 N m^{−1} and natural length 10 cm. The system rests on a smooth horizontal table. If the charge on each particle is 2.0 × 10^{−8} C, find the extension in the length of the spring. Assume that the extension is small as compared to the natural length. Justify this assumption after you solve the problem.

Two particles A and B, each carrying a charge Q, are held fixed with a separation dbetween them. A particle C of mass m and charge q is kept at the middle point of the line AB. If it is displaced through a distance x perpendicular to AB, what would be the electric force experienced by it?

Two particles A and B possessing charges of +2.00 × 10^{−6} C and of −4.00 × 10^{−6} C, respectively, are held fixed at a separation of 20.0 cm. Locate the points (s) on the line AB, where (a) the electric field is zero (b) the electric potential is zero.

A point charge produces an electric field of magnitude 5.0 NC^{−1} at a distance of 40 cm from it. What is the magnitude of the charge?

**Answer the following question.**

Define a unit charge.

**Answer the following question.**

What is relative permittivity?

**Solve numerical example.**

Three equal charges of 10×10^{-8} C respectively, each located at the corners of a right triangle whose sides are 15 cm, 20 cm, and 25cm respectively. Find the force exerted on the charge located at the 90° angle.

Write down Coulomb’s law in vector form and mention what each term represents.

What are the differences between the Coulomb force and the gravitational force?

Write a short note on superposition principle.

Explain in detail Coulomb’s law and its various aspects.

Three charges +Q, q, +Q are placed respectively, at distance, 0, d/2 and d from the origin, on the X-axis. If the net force experienced by +Q, placed at x = 0, is zero then value of q is ____________.

A force F acts between sodium and chlorine ions of salt (sodium chloride) when put 1 cm apart in air. The permittivity of air and dielectric constant of water are `epsilon_0` and K respectively. When a piece of salt is put in water, electrical force acting between sodium and chlorine ions 1 cm apart is ____________.

The force between two charges 0.06 m apart is 5 N. If each charge is moved towards the other by 0.01 m, then the force between them will become ____________.

The electric force acting between two point charges kept at a certain distance in vacuum is 16 N. If the same two charges are kept at the same distance in a medium of dielectric constant 8, the electric force acting between them is ____________ N.

A total charge Q is broken in two parts Q_{1} and Q_{2} and they are placed at a distance R from each other. The maximum force of repulsion between them will occur, when ____________.

Two point charges +3 µC and +8 µC repel each other with a force of 40 N. If a charge of -5 µC is added to each of them, then force between them will become ______.

The ratio of the forces between two small spheres with constant charge (a) in air (b) in a medium of dielectric constant K is ______.

Two charges of equal magnitudes kept at a distance r exert a force F on each other. If the charges are halved and distance between them is doubled, then the new force acting on each charge is ______.

A spring of spring constant 5 × 10^{3} N/m is stretched initially by 5 cm from the unstretched position. Then the work required to stretch it further by another 5 cm is:

Coulomb's law is given by F = k q_{1}q_{2} r^{n} where n is

Two charge – 10c and + 10 c are placed 10 cm apart. Potential at centre of the line joining the two charge is:-

The capacity of an isolate conducting sphere of radius R is proportional to

The S.I unit of electric permittivity is

Identify the wrong statement in the following.

Coulomb's law correctly describes the electric force that ______

Electric charge of any system is ______.

Two point charges Q each are placed at a distance d apart. A third point charge q is placed at a distance x from the mid-point on the perpendicular bisector. The value of x at which charge q will experience the maximum Coulomb's force is ______.

The ratio of the forces between two charges placed at a certain distance apart in the air and by the same distance apart in a medium of dielectric constant K is ______.

Two point charges +2 C and +6 C repel each other with a force of 12 N. If a charge of -4 C is given to each of these charges, then the force now is ______.

Four charges equal to - Q are placed at the four a corners of a square and charge q is at its centre. If the system is in equilibrium, the value of q is ______.