Question

A manufacturer claims that a carpet will not generate more than 5.8 kV of static electricity What magnitude of charge would have to be transferred between a carpet and a shoe for there to be a 5.8 kV potential distance d = 2.8 mm ? Approximate the area of a shoe as 30 cm x 8 cm. Express your answer using two significant figures.

Answer 1

4.4×10⁻⁷ Coulomb

Step-by-step explanation:

V = Voltage = 5.8 kV

d = Potential distance = 2.8 mm = 0.0028 m

A = Area = 0.3×0.08 = 0.024 m²

ε₀ = permittivity constant in a Vacuum= 8.85×10⁻¹² F/m

`(Q)/(V)=(A\epsilon_0)/(d)\\\Rightarrow \Q=V(A\epsilon_0)/(d)\\\Rightarrow Q=5.8* 10^3(0.024* 8.85* 10^(-12))/(0.0028)\\\Rightarrow Q=4.4* 10^(-7)\ C`

Magnitude of charge transferred between a carpet and a shoe is 4.4×10⁻⁷ Coulomb.