Answer:
Qsinθ/4πε₀R²θ
Explanation:
Let us have a small charge element dq which produces an electric field E. There is also a symmetric field at P due to a symmetric charge dq at P. Their vertical electric field components cancel out leaving the horizontal component dE' = dEcosθ = dqcosθ/4πε₀R² where r is the radius of the arc.
Now, let λ be the charge per unit length on the arc. then, the small charge element dq = λds where ds is the small arc length. Also ds = Rθ.
So dq = λRdθ.
Substituting dq into dE', we have
dE' = dqcosθ/4πε₀R²
= λRdθcosθ/4πε₀R²
= λdθcosθ/4πε₀R
E' = ∫dE' = ∫λRdθcosθ/4πε₀R² = (λ/4πε₀R)∫cosθdθ from -θ to θ
E' = (λ/4πε₀R)[sinθ] from -θ to θ
E' = (λ/4πε₀R)[sinθ]
= (λ/4πε₀R)[sinθ - sin(-θ)]
= (λ/4πε₀R)[sinθ + sinθ]
= 2(λ/4πε₀R)sinθ
= (λ/2πε₀R)sinθ
Now, the total charge Q = ∫dq = ∫λRdθ from -θ to +θ
Q = λR∫dθ = λR[θ - (-θ)] = λR[θ + θ] = 2λRθ
Q = 2λRθ
λ = Q/2Rθ
Substituting λ into E', we have
E' = (Q/2Rθ/2πε₀R)sinθ
E' = (Q/θ4πε₀R²)sinθ
E' = Qsinθ/4πε₀R²θ where θ is in radians
Physical changes are those change which just externally or physically change the state of the object . for example : water boils and evaporates... here the state is just changing from liquid to vapour while the composition is the same.
chemical changes are those which bring about a change in the composition of a substance. for example: burning of paper changes into ash .
Answer:
A. Increasing the voltage of the battery
Explanation:
The relationship between voltage, V, current, I and resistance, R, is given as follows;
V = I × R
∴ I = V/R
From the above relationship, the current flowing in the circuit is directly proportional to the voltage of the battery, and inversely proportional to the resistance, 'R', of the circuit
Therefore, increasing the voltage, 'V', of the battery, increases the total current, 'I', flowing in the circuit.
Answer:
1.2 amps :)
Explanation:
A heater has a resistance of 10.0 Ω. It operates on a 12.0 V. What is the current through the resistor?
Known:
Unknown:
I = V/R
= 12.0 V / 10.0 Ω
= 1.2 amps
Answer:
137200000 watts or 137200 kilowatts
Explanation:
The formula for power is P= dhrg
Where P = Power in watts
d = density of water (1000 kg/m^3)
h = height in meters
r = flow rate in cubic meters per second,
g = acceleration due to gravity of 9.8 m/s^2,
Plugging in the known values,
we get
P = 1000 kg/m^3 * 80 m * 175 m^3/s * 9.8 m/s^2
P = 80000 kg/m^2 * 175 m^3/s * 9.8 m/s^2
P = 14000000 kg m/s * 9.8 m/s^2
P = 137200000 kg m^2/s^3
P = 137200000 watts or 137200 kilowatts
The above figure assumes 100% efficiency which is impossible. A good efficiency would be 90% so the actual power available would be close to 0.90 * 137200 = 123480 kilowatts
