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 [ M^{0}L^{0}T^{1}A^{1} ]
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^{०}
∴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^{०}
∴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^{०}
∴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 = A_{x}B_{x} + A_{y}B_{y} + A_{z}B_{z}
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
- Cross product of two vectors in not commutative.
$$ \vec{A} \times \vec{B} = – \vec{B} \times \vec{A}$$ - 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 A_{m} and the error in measurement be ΔA. Then the true value of the quantity can be written as
A_{t} = A_{m} ± 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
- Systematic errors
- Random errors
- 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 [ M^{1}L^{2}T^{-2} ]. SI unit of work is joule. CGS unit of work is erg.
Relation between joule and erg is
1 joule = 10^{7} erg.
In terms of rectangular components, work is
W = x F_{x} + y F_{y} + z F_{z}
Types of work
Positive work
If angle between \(\vec{F}\) and \(\vec{S}\) lies between 0^{0} and 90^{0}, then work done is positive.
Negative work
If angle between \(\vec{F}\) and \(\vec{S}\) lies between 90^{0} and 180^{0}, 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 90^{0}
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 |