Physics Solved Problems: Electrostatics and Resistance
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Electrostatics and Resistance Solved Problems
Point of Zero Electric Field Intensity
Vicinity Equal to Zero:
Q1 = -20 × 10-6 C, Q2 = +5 × 10-6 C, r = 2 m
r1 = (2 + x) m, r2 = x m
The electric field intensity at P due to Q1:
E1 = (1 / 4πε0) × (Q1 / r12)
= (9 × 109 × 20 × 10-6) / (2 + x)2
The electric field intensity at P due to Q2:
E2 = (1 / 4πε0) × (Q2 / r22)
= (9 × 109 × 5 × 10-6) / x2
At P, E = 0, therefore E1 = E2:
(9 × 109 × 20 × 10-6) / (2 + x)2 = (9 × 109 × 5 × 10-6) / x2
4 / (2 + x)2 = 1 / x2
(2 / (2 + x))2 = (1 / x)2
2x = 2 + x
x = 2 m
Electric Properties of a Uranium Nucleus
Uranium:
e = 1.6 × 10-19 C, r = 10-10 m
Q = 9.2e
= 9.2 × (1.6 × 10-19 C)
= 14.72 × 10-19 C
(i) Electric Field (E):
E = (1 / 4πε0) × (Q / r2)
= (9 × 109 × 14.72 × 10-19) / (10-10)2
= 1.3248 × 109 N/C
The direction of the electric field is away from the nucleus.
(ii) Force (F):
F = eE
= (1.6 × 10-19 C) × (1.3248 × 109 N/C)
= 2.1196 × 10-10 N
The direction of the force is towards the nucleus.
(iii) Potential (V):
V = (1 / 4πε0) × (Q / r)
= (9 × 109 × 14.72 × 10-19) / 10-10
= 1.3248 V
Resistance and Wire Stretching Calculations
Find Resistance:
r = d / 2 = (2 × 10-3) / 2 = 1 × 10-3 m
R = ρl / A = 1.528 Ω
Wire Stretching Problem:
R = 10 Ω, L' = 2L, R' = ?
Before stretching:
R = ρ L / A
After stretching:
R' = ρ L' / A'
Since the wire has the resistivity and density unchanged, the volumes remain the same:
V = V'
A L = A' L'
A L = A' (2L)
A' = A / 2
R' = ρ L' / A'
R' = ρ (2L) / (A / 2)
R' = ρ × 4L / A
R' = 4 × 10
R' = 40 Ω
Galvanometer Conversion Calculations
Given: Rg = 20 Ω, i = 5 mA = 5 × 10-3 A, I = 1 A
(i) Conversion to Ammeter:
r = (i × Rg) / (I - i)
r = (5 × 10-3 × 20) / (1 - 5 × 10-3)
r = 0.1 Ω
The shunt of resistance r = 0.1 Ω is connected in parallel.
(ii) Conversion to Voltmeter (V = 100V):
R = (V / i) - Rg
R = (100 / (5 × 10-3)) - 20
R = 19980 Ω
The high resistance R = 19980 Ω is connected in series.
Fundamental Physics Definitions
- Electric Field Intensity: The electric field intensity at a point in an electric field is the electric force acting upon a unit positive charge placed at that point.
- Equipotential Surface: A surface drawn through points at the same potential is called an equipotential surface.
- Photoelectric Current: Photoelectric current is directly proportional to the intensity of the incident light.
- Photon Energy: The energy of a photon is related to the frequency of light.
- Hubble Time: Hubble time is the reciprocal of the Hubble constant.
- Redshift Formula: Redshift formula: