Chapter 1:- Electric Charges and feilds.
ASSIGNMENT
Chapter 1: Electric Charges and Fields
Charge:
- Charge of the body is the property due to which it interacts with other charges.
- Charge is a scalar quantity.
- SI unit of charge is coulomb (C).
- The fundamental charges available in the universe are electron and proton.
- Charge on 1e- is -1.6 × 10-19 C
- Charge on 1p+ is +1.6 × 10-19 C
Note:
- Mass of 1e- is 9.1 × 10-31 kg
- Mass of 1p+ is 1.67 × 10-27 kg
- Charges are of two types: positive and negative.
Properties of Charges:
- Some charges repel each other (like), and opposite charges attract each other (unlike).
Note: When there are two forces, gravitational force and electrostatic force, among them we neglect gravitational force because it is quite weak compared to electrostatic force.
2) Quantisation of Charge:
- Charge on the body is always an integral multiple of e, which is called the Quantisation of charge.
- Formula: Q = ne
- Where n = integer = 1, 2, 3, ...
3) Additivity of Charges:
- Charges can be added like scalar quantities, i.e., algebraically.
4) Conservation of Charge:
- The algebraic sum of electric charges in an electrically isolated system always remains constant, irrespective of any process taking place.
Note: Some amount of positive and negative charges can be produced or destroyed in an isolated system during a process, but the final amount of charge remains constant.
Numerical Questions:
Q-1: Q = 3.2 × 10-7 C, n = ?
We use the formula: Q = ne
⇒ n = Q / e
⇒ n = (3.2 × 10-7) / (1.6 × 10-19)
⇒ n = 2 × 1012
Q-2: 1 C charge = ? e-
Again, use Q = ne
1 = n × (1.6 × 10-19)
⇒ n = 1 / (1.6 × 10-19)
⇒ n = 6.25 × 1018
Q-3: Define 1 coulomb charge
If there are 6.25 × 1018 electrons, then charge on the system is 1 coulomb.
Q-4: Q = 5.8 × 10-18 C, is it possible?
Check if Q is an integral multiple of e:
n = Q / e
⇒ n = (5.8 × 10-18) / (1.6 × 10-19)
⇒ n = 36.25
Since the charge is not an integral multiple of e, it is not possible.
Electroscope
Electroscope is the device which detects the presence of charge.
- We can detect amount of charge whether it is low or high, but not its exact quantity.
- We cannot detect whether the charge is positive or negative, i.e., it is electron or proton.
Construction of an Electroscope:
- In an electroscope, a metallic rod is fixed inside an electrically isolated system from the end where two golden leaves are attached.
- Another end of the rod, i.e., outside the system, is attached to a metallic knob.
Diagram:
★ Working of an Electroscope:
- When an electrically charged body with any of the charges on it is brought to contact with the metallic knob, the charge travels down to the golden leaves through the metallic rod.
- When the charge reaches the golden leaves, it is further distributed to both of them.
- Later, since the charge is distributed to both leaves, they both contain some charge and thus repel each other.
Diagram:
★ Different Methods of Charging:
- By Contact
Illustration:
★ Different Methods of Charging:
- By Contact
Illustration:
- By Friction
Example:
Glass rod rubbed with Silk → Electrons transfer from glass to silk Glass: → loses e- → becomes positively charged Silk: → gains e- → becomes negatively charged
Diagram:
Note: Glass gives e-
Another Example:
Plastic rubbed with Wool → Electrons transfer from wool to plastic Plastic: Gains e- (negative) Wool: Loses e- (positive)
Note: Wool accepts e-
★ Electrostatic Force Between Two Charges
Formula:
F = K × (q1 × q2) / r²
Where:
- K = Coulomb’s Constant = 9 × 10⁹ Nm²/C²
- K = 1 / (4πε0)
- ε0 = Permittivity of Free Space = 8.854 × 10⁻¹² C²/N·m²
Definition:
The force acting between two stationary point charges is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them. The force acts along the line joining the two charges.
Force in Vacuum:
F = (1 / 4πε0) × (q1 × q2) / r²
Force in Medium:
Fm = (1 / 4πε) × (q1 × q2) / r²
- ε = Permittivity of the Medium
Relation between Forces:
F / Fm = ε / ε0 = K
- K = Dielectric Constant of the Medium
Also,
Fm = F / K