Solved Examples on Charge Flow

Problem 1: The density of free electrons in a copper conductor is estimated to be 8.5 x 10²⁸ m^-3. How long does an electron take to drift from one end of a wire 3.0 m long to its other end? The area of the cross-section of the wire is 2.0 x 10^-6m² and it carries a current of 3.0 A.

Solution:

Density of free electron in a copper conductor, n = 8.5 x 10²⁸ m^-3

Length of the copper wire, l = 3.0 m

Area of cross-section of the wire, A = 2.0 x 10^-6 m²

Current carried by the wire, I = 3.0 A, which is given by,

I=nAeV_d 

Where,

e = Electric charge = 1.6 x 10^-19 C

V_d = Drift velocity = Length of the wire(l) / Time taken to cover l(t)

I = nAe(l/t)

t = nAel/I

t = 3 x 8.5 x 10²⁸ x 2 x 10^-6 x 1.6 x 10^-19 / 3.0

t = 2.7 x 10⁴ s

Hence, the time taken by an electron to drift from one end of the wire to the other is 2.7 x 10⁴ s. 

Problem 2: Force F is acting between two-point charges. If a sheet of metal (ε_r= 8) is placed between these charges, then what will be the force?

Solution:

We know, 

F = ( 1/(4 π ϵ₀K)) ( |q1| |q2| / r²) 

= F/K 

= F/6

Problem 3: A charge of 5.60 x 10^-3 C is placed at one end of the 8.37 km sandcastle, while an unspecified charge is placed at the opposite end. If the electrical potential energy associated with these charges is -50.5 J, what is the quantity of the second charge?

Solution: 

PE_electric = -50.5 J

q₂ = 5.60 x 10^-3 C

r = 8.37 km = 8.37 x 10³ m

k_c = 8.99 x 10⁹ Nm²/C²

To find : q1

Equation for the electrical potential energy associated with a pair of charges. 

q₁  = r PE_electric / k_c q₂

q₁ = (8.36 x 10³) (-50.5) / (8.99 x 10⁹) (5.60 x 10^-3) C

q₁ = 8.40 x 10^-3

The quantity of the second charge = 8.40 x 10^-3 C.

Problem 4: A potentiometer wire has a length of 1.5 m and a resistance of 10 Ω. It is connected in series with the cell of emf 4 volt and internal resistance 5 Ω. Calculate the potential drop per centimeter of the wire. 

Solution: 

Given: L = 1.5m, R = 10 Ω, E = 4 V, r = 5 Ω. 

K = ER / (R + r) L

K = 4 x 10 / (10 + 5) 1.5

K = 400/225  V/m

K = 400/22500  V/cm = 0.0178 V/cm 

The potential drop per centimeter of the wire if 0.0178 V/cm.

Electricity is the flow of electric charges through a metal. All charges present in a conductor whether free or bound, are considered to be at rest. Electric Charge is the property of a matter due to which it experiences and produces electrical and magnetic effects. Charges in motion produce an electric current. Such current occurs in many situations under certain circumstances. If an electric field is applied to an electric charge, it will experience a force. It will move if it is free to do so, generating a current. There exist two types of charges in nature, positive charge and negative charge. Charges with the same electrical sign repel each other and those with the opposite electrical sign attract each other. The S.I. unit of charge is coulombs (C).