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 ]

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 = 0


A.B = AB
For unit vectors,

î . î = ĵ . ĵ = k.k = 1


•   If two vectors A and B are mutually perpendicular, then θ = 90

A.B = 0

For unit vectors,

î . ĵ = ĵ . k = k.i = 0


•   If two vectors A and B are anti parallel, then θ = 0


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 . B = AxBx + AyBy + AzBz

Cross Product of two vector

Cross product of two \( \vec{A}\) and \( \vec{B}\) is represented by,

$$ \vec{A} \times \vec{B} = A B \sin \theta \hat{n}$$

Where \( \hat{n}\) is the unit vector along the resultant vector.

If two vectors \( \vec{A}\) and \( \vec{B}\) are parallel,

Then $$ \theta = 0^o or 180^o$$
So $$ \vec{A} \times \vec{B} = 0$$

For unit vectors

$$ \hat{i} \times \hat{i} = \hat{j} \times \hat{j} = \hat{k} \times \hat{k} = 0$$

If two vectors \( \vec{A}\) and \( \vec{B}\) are perpendicular,

Then $$ \theta = 90^0$$
So $$ \vec{A} \times \vec{B} = AB \hat{n}$$

For unit vectors
\( \hat{i} \times \hat{j} = \hat{k}\) , \( \hat{j} \times \hat{k} = \hat{i}\) , \( \hat{k} \times \hat{i} = \hat{j}\)

Properties of cross product

  1. Cross product of two vectors in not commutative.
    $$ \vec{A} \times \vec{B} = – \vec{B} \times \vec{A}$$
  2. Cross product is distributive.
    $$ \vec{A} \times ( \vec{B} + \vec{C} ) = \vec{A} \times \vec{B} + \vec{A} \times \vec{C}$$

Cross product of two vectors \( \vec{A}\) and \( \vec{B}\) in component form

$$ \vec{A} \times \vec{B} = ( A_y B_z – A_z B_y ) \hat{i} +
( A_z B_x – A_x B_z ) \hat{j} + ( A_x B_y – A_y B_x ) \hat{k}$$

What is the errors of measurement in physics?

What is the errors of measurement in physics?

Errors of measurement = True value of a quantity – Measured value of a quantity

Suppose, the measured value of quantity be Am and the error in measurement be ΔA. Then the true value of the quantity can be written as
At = Am ± ΔA

Absolute error, Relative error and Percentage error

Absolute error

Suppose a physical quantity be measured n times and the measured values be \( a_1, a_2, a_3 — a_n \). The arithmetic mean of these values is given by,

$$ a_m = \frac{a_1 + a_2 + a_3 + … + a_n }{n}$$

The absolute errors in the individual measurement values are

$$ \Delta a_1 = a_m – a_1 $$

$$ \Delta a_2 = a_m – a_2 $$

$$ \Delta a_3 = a_m – a_3 $$

………….

$$ \Delta a_n = a_m – a_n $$

Mean absolute error

Mean absolute error \( \Delta a_m\) of a physical quantity is given by,

$$ \Delta a_m = \frac {|\Delta a_1| + |\Delta a_2| + |\Delta a_3| +…+ |\Delta a_n|}{n} $$

Relative error

Relative error \( R_e\) is given by,

$$ \ R_e = \frac{\Delta a_m}{a_m}$$

Percentage error

Percentage error \( p_e\) is given by,

$$ P_e = \frac{\Delta a_m}{a_m} \times 100 \% $$

Types of errors

  1. Systematic errors
  2. Random errors
  3. Gross errors

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