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What is an electric charge?

Charge is the properties of matter. According to Benjamin franklin there are two types of charge, (1) Positive charge and (2) Negative charge.
Electric charge is a scalar quantity.
In SI System, the unit of Electric charge is Coulomb.
The dimensional formula of Electric charge is [ M0L0T1A1 ]

Coulomb's law
The force on a test charge Q due to a single point charge q is given by coulomb's law $$\vec{F} = \frac{1}{4\pi \epsilon_0 } \frac{Qq}{r^2} \hat{r}$$ Where r is the distance between Q and q and ε0 is the permitivity of the free space.

Electric field
The force per unit charge that would be exerted on a test charge is called electric field.

Electric flux
$$\Delta \phi = \vec{E}.\Delta S$$

Gauss's law
Electric flux ( φ ) through a closed surface (S) enclosing the total charge (q) is given by,
$$\phi = \frac{q}{\epsilon_0}$$
That is is the Gauss's law.

Electric dipole
If two equal and opposite charges +q and -q are separated by a distance 2d, then this arrangement is called electric…

What is scalar and vector quantity?

The physical quantity which have only magnitude but no direction, are called scalar quantity.
Mass, length, time, speed, volume, density, pressure, temperature, work, energy, power, electric current, electric charge, electric potential, electric flux etc are the examples of scalar quantity.


Scalar or Dot Product
Dot product of two vectors A and B is represented by,
A .B = AB cosθ


Where θ is angle between two vectors A and B.

•   If two vectors A and B are parallel, then θ = 0०


A.B = AB
For unit vectors,

î . î = ĵ . ĵ = k.k = 1


•   If two vectors A and B are mutually perpendicular, then θ = 90०

A.B = 0

For unit vectors,

î . ĵ = ĵ . k = k.i = 0


•   If two vectors A and B are anti parallel, then θ = 0०


A.B = - AB

•   Properties of dot product


1.Dot product of two vectors is commutative.

A . B = B . A

2.Dot product is distributive.

A . ( B + C ) = A . B + A . C

•   Dot product of two vectors A and B in component form
A .…

What is work in physics?

What is work?
Scalar product of force and displacement is called work.
$$ W = \vec{F}.\vec{S}\cos \theta $$
Work is a scalar quantity. The dimensional formula of work is [ M1L2T-2 ]. SI unit of work is joule. CGS unit of work is erg.
Relation between joule and erg is
1 joule = 107 erg.
In terms of rectangular components, work is
W = x Fx + y Fy + z Fz
Types of work
Positive work
If angle between \(\vec{F}\) and \(\vec{S}\) lies between 00 and 900, then work done is positive.
Negative work
If angle between \(\vec{F}\) and \(\vec{S}\) lies between 900 and 1800, then work done is negetive.
Negative work
The work done is zero, if

there is no displacement
no force is acting on the body
angle between \(\vec{F}\) and \(\vec{S}\) is 900

What is the position vector of centre of mass of the two particle system?

For two particle system, the position vector of centre of mass of the two particle system is given by,
$$\vec{r} = \frac {m_1 \vec{r_1} + m_2 \vec{r_2}}{m_1+m_2}$$

For two particle system, velocity of centre of mass is given by,
$$\vec{v_c} = \frac {m_1 \vec{v_1} + m_2 \vec{v_2}}{m_1+m_2}$$
Whewe,
\(m_1\) and \(m_2\) are the masses of two particles.
\(\vec{r_1}\) and \(\vec{r_2}\) are the position vector of the particles \(m_1\) and \(m_2\) respectively.
\(\vec{v_1}\) and \(\vec{v_2}\) are velocities of the particles \(m_1\) and \(m_2\) respectively.

What is logic gates?

Truth table of AND Gate:



INPUT
OUTPUT



A
B
Y = A.B


0
0
0


0
1
0


1
0
0


1
1
1



Truth table of NOT Gate.



INPUT
OUTPUT


A
Y
0
1
1
0


Truth table of OR Gate.

INPUT
OUTPUT
A
B
Y = A+B
0
0
0
0
1
1
1
0
1
1
1
1



Truth table of NAND Gate.

INPUT
OUTPUT
A
B
Y

0
0
1

0
1
1

1
0
1

1
1
0



Truth table of NOR Gate.



INPUT
OUTPUT
A
B
Y

0
0
1

0
1
0

1
0
0

1
1
0




Truth table of XOR Gate.



INPUT
OUTPUT
A
B
Y

0
0
0

0
1
1

1
0
1

1
1
0