Answer:
(a) 1.15×10⁻⁸ F.
(b) 1.5×10⁻⁸ C.
Step-by-step explanation:
(a)
Capacitance of a capacitor: This is the ability for a capacitor to store charge.
The S.I unit of capacitance of a capacitor is Farad (F).
Mathematically, it is represented as
C = ε₀A/d² ................. Equation 1
Where C = Capacitance of the capacitor, ε₀ = permitivity of free space, A = area of the plates, d = distance between the plates.
Given: A = 1×10⁶ m². d = 770 m
Constant: ε₀ = 8.85×10⁻¹² F/m
Substituting these values into equation 1
C = 8.85×10⁻¹²(1×10⁶ )/770
C = 8.85×10⁻⁶/770
C= 0.0115×10⁻⁶
C = 1.15×10⁻⁸ F.
Thus the capacitance of the cloud layer = 1.15×10⁻⁸ F.
(b)
Electric Field Strength: This is the force per unit charge which is exerted at a point in a in a electric field.
It can be represented mathematically as
E = kq/d²........................... Equation 2
Where E = Electric Field Strength, q = charge, d = distance. k = proportionality constant.
Making q the subject of the equation above,
q = Ed²/k ........................... Equation 3.
Given: E = 2×10⁶ N/C, d = 770 m
Constant: k = 1/4πε₀ = 9×10⁹ Nm²/C²
Substituting these values into equation 3
q = 2×10⁶(770)²/(9×10⁹)
q = (2×10⁶)(592900)/(81×10¹⁸)
q = 14639.5×10⁻¹²
q ≈ 1.5×10⁻⁸ C.
Thus the charge the cloud can hold = 1.5×10⁻⁸ C.
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