Electric Line of Force and its Properties

Electric Field:

That region around any charged particle (source-charge) in which other test charged particle experience an electric force (attraction or repulsion). This region is called electric field of that charged particle.

The size and magnitude of the test charged particle is very small i.e tends to zero which does not modify the electric field of source charged particle. The electric field can only experience, not be seen by eyes. The electric field is defined by imaginary lines which are called electric field lines.

Electric Field Lines:

Electric field lines are imaginary lines that describe the behavior of electric fields. The behavior of the electric field tells about the force acting on free test-charged particles. This force gives the motion to the free test charge particle which is placed in the path of the electric field line. So the test charged particle moves in the direction of the electric field line. Hence, the direction of electric force and electric field lines both are the same. Thus electric field line is also known as electric lines of force.

Electric Lines of Force:

An electric line of force is defined as an imaginary smooth curve drawn in electric field along which a free isolated test charged particle moves. The tangent drawn at any point on the electric line of force gives the direction of the force acting on a test charged particle placed at that point.

Properties of Electric Line of Force:

There are the following properties of the electric line of force:

1.) The direction of the electric line of force is outward for positively charged particles, and inward for negatively charged particles.
 Electric field line of positive charge

 Electric field line of negative charge

So when two opposite charge are placed near each other, the electric line of force start from a positive charge and end at a negative charge
 Electric lines of force of unlike charges
When two same nature charges are placed near each other, the field produced by one charge is equal and opposite to the field produced by the other charges at the midpoint of the line joining the two charges. Therefore, at this point, the resultant electric field is zero. This point is called the neutral point.
 Electric lines of force of like charges

2.) The tangent drawn at any point on the line of force gives the direction of the force acting on a test-charged particle at that point.

3.) Two electric lines of force can never intersect with each other because if they do so then at the point of intersection two tangents can be drawn which would mean that there are two directions of the force at that point which is impossible.

4.) When electric lines of force are closer to each other, the electric field is stronger in this region. And where The line of force are far away from each other then the electric field is weaker in this region. When the line of force are parallel and in a straight line to each other, the electric field is known as the uniform electric field.

5.) The electric line of force has a tendency to contract in length like a stretched elastic string for the opposite nature of the charged particle. It is due to the attraction force between charged particles.

6.) The electric line of force has a tendency to separate from each other in the direction perpendicular to their length for the same nature of charged particles. It is due to the repulsion force between charged particles.

7.) The electric lines of force can never form closed loops as a line can never start and end on the same charge.

8.) The electric line of force also gives us an indication of the equipotential surface (That surface which has the same potential on each point of the surface).

9.) The electric line of force always flows from higher potential to lower potential.

10.) In a region where there is no electric field, lines are absent so the electric field inside the conductor is zero. Electric lines of force end or start normally from the surface of a conductor.

Numerical Aperture and Acceptance Angle of the Optical Fibre

Angle of Acceptance → If incident angle of light on the core for which the incident angle on the core-cladding interface equals the critical angle then incident angle of light on the core is called the "Angle of Acceptance. Transmission of light when the incident angle is equal to the acceptance angle If the incident angle is greater then the acceptance angle i.e. $\theta_{i}>\theta_{0}$ then the angle of incidence on the core-cladding interface will be less than the critical angle due to which part of incident light is transmitted into cladding as shown in the figure below Transmission of light when the incident angle is greater than the acceptance angle If the incident angle is less then the acceptance angle i.e. $\theta_{i}<\theta_{0}$ then the angle of incidence on the core-cladding interface will be greater than the critical angle for which total internal reflection takes place inside the core. As shown in the figure below Transmission of light w

Fraunhofer diffraction due to a single slit

Let $S$ be a point monochromatic source of light of wavelength $\lambda$ placed at the focus of collimating lens $L_{1}$. The light beam is incident normally from $S$ on a narrow slit $AB$ of width $e$ and is diffracted from it. The diffracted beam is focused at the screen $XY$ by another converging lens $L_{2}$. The diffraction pattern having a central bright band followed by an alternative dark and bright band of decreasing intensity on both sides is obtained. Analytical Explanation: The light from the source $S$ is incident as a plane wavefront on the slit $AB$. According to Huygens's wave theory, every point in $AB$ sends out secondary waves in all directions. The undeviated ray from $AB$ is focused at $C$ on the screen by the lens $L_{2}$ while the rays diffracted through an angle $\theta$ are focussed at point $p$ on the screen. The rays from the ends $A$ and $B$ reach $C$ in the same phase and hence the intensity is maximum. Fraunhofer diffraction due to

Particle in one dimensional box (Infinite Potential Well)

Let us consider a particle of mass $m$ that is confined to one-dimensional region $0 \leq x \leq L$ or the particle is restricted to move along the $x$-axis between $x=0$ and $x=L$. Let the particle can move freely in either direction, between $x=0$ and $x=L$. The endpoints of the region behave as ideally reflecting barriers so that the particle can not leave the region. A potential energy function $V(x)$ for this situation is shown in the figure below. Particle in One-Dimensional Box(Infinite Potential Well) The potential energy inside the one -dimensional box can be represented as $\begin{Bmatrix} V(x)=0 &for \: 0\leq x \leq L \\ V(x)=\infty & for \: 0> x > L \\ \end{Bmatrix}$ $\frac{d^{2} \psi(x)}{d x^{2}}+\frac{2m}{\hbar^{2}}(E-V)\psi(x)=0 \qquad(1)$ If the particle is free in a one-dimensional box, Schrodinger's wave equation can be written as: $\frac{d^{2} \psi(x)}{d x^{2}}+\frac{2mE}{\hbar^{2}}\psi(x)=0$ \$\frac{d^{2} \psi(x)}{d x