Electric Field in Material MCQ Quiz - Objective Question with Answer for Electric Field in Material - Download Free PDF

Ans. (3) Sol.

Given:

V = 3 volts

R = 1.5 Ω

e = 1.6 × 10⁻¹⁹ C

t = 1 s

Now, Current I = V / R = 3 / 1.5 = 2 A

Also, I = Q / t = (n × e) / t

So, n = (I × t) / e = (2 × 1) / (1.6 × 10⁻¹⁹) = 1.25 × 10¹⁹

Concept:

The number of electrons transferred when a charge is rubbed or moved can be calculated using the formula:

Q = n × e

Where:

• Q = total charge transferred
• n = number of electrons transferred
• e = elementary charge = 1.6 × 10^-19 C

Rearranging the formula to find the number of electrons:

n = Q / e

Calculation:

Given:

• Q = 3.52 × 10^-7 C
• e = 1.6 × 10^-19 C

n = (3.52 × 10^-7) / (1.6 × 10^-19) = 2.2 × 10¹² electrons

∴ The number of electrons transferred is 2.2 × 10¹².

Additional Information 

• Electric Displacement Field (D): The normal component of the electric displacement field (D) is continuous across the boundary between two dielectrics if there are no free charges at the interface.  If there are free charges, the difference in the normal components of D is equal to the surface charge density.   
• Electric Field (E): The tangential component of the electric field (E) is continuous across the boundary.  However, the normal component of E is discontinuous due to the difference in permittivities of the two materials.   
• Magnetic Field (H): The tangential component of the magnetic field (H) can be discontinuous at the boundary. The discontinuity is related to the surface current density at the interface. The normal component of B (magnetic flux density) is always continuous.   
• Current Density (J): Current density is related to the flow of charge.

Calculation:

The resistance R of a conductor is given by:

\( R = \frac{\rho L}{A}\)

\( \rho\): is the resistivity of the material,

L: is the length of the conductor,

A:  is the cross-sectional area.

Since both conductors A and B are made of the same material and have the same length, the ratio of resistances depends on their cross-sectional areas.

Conductor A is a solid cylinder with diameter 1m, so its radius is:

\(r_A = \frac{1}{2} = 0.5 \text{ m}\)

The cross-sectional area is:

\( A_A = \pi r_A^2 = \pi (0.5)^2 = \frac{\pi}{4} \text{ m}^2\)

Conductor B is a hollow cylinder (tube) with inner diameter 1m and outer diameter 2m. The inner radius is:

\( r_{\text{inner}} = \frac{1}{2} = 0.5 \text{ m}\)

The outer radius is:

\( r_{\text{outer}} = \frac{2}{2} = 1 \text{ m}\)

The cross-sectional area is:

\( A_B = \pi (r_{\text{outer}}^2 - r_{\text{inner}}^2)\)

\(A_B = \pi (1^2 - 0.5^2) = \pi (1 - 0.25) = \frac{3\pi}{4} \text{ m}^2\)

Since \(R \propto \frac{1}{A}\), the ratio of resistances is:

\( \frac{R_A}{R_B} = \frac{A_B}{A_A} = \frac{\frac{3\pi}{4}}{\frac{\pi}{4}} = 3\)

Thus, option '4' is correct.

• According to Maxwell's equations, at the boundary separating two media, the tangential components of the electric field E and the magnetic field H are continuous across the boundary, provided there are no surface currents or charges on the boundary.
• The tangential components of both E and H are continuous when there are no surface currents or charges.
   
  Additional Information

Law of magnetic flux reflection:

• The relationships existing between the magnetic field strengths and flux densities at the boundary are called the boundary conditions.
• There are discontinuities in magnetic fields at the boundaries between conductors and material of different permeability.

• The normal component of flux density is continuous across the boundary.
  B1n = B2n
• The second boundary condition is that the tangential field strength is continuous across the boundary.
  H1t = H2t
   

The boundary condition for electrostatic fields are defined as:

• E1t = E2t (Tangential components are equal across the boundary surface)
• Also, the normal component satisfies the following relation:
• D1n – D2n = ρs
• For a charge-free boundary, ρs = 0, the above expression becomes:
• D1n – D2n = 0
• D1n = D2n

Option 2 is correct, i.e. Conductance.

Conductance:

• The degree to which an object conducts electricity, calculated as the ratio of the current which flows to the potential difference present.
• This is the reciprocal of the resistance and is measured in siemens or mhos.

Note:

Conductivity:

• Electrical conductivity is the measure of the amount of electrical current a material can carry or its ability to carry a current.
• It is also known as specific conductance.
• It is an intrinsic property of a material.
• It is denoted by the symbol σ and has SI units of Siemens per meter (S/m).

Resistivity (ρ):

• Resistivity is the resistance per unit length and cross-sectional area.
• It is the property of the material that opposes the flow of charge or the flow of electric current.
• The unit of resistivity is ohm meter.
• A material with high resistivity means it has got high resistance and will resist the flow of electrons.
• A material with low resistivity means it has low resistance and thus the electrons flow smoothly through the material.
• It depends on the material of the conductor but not on its dimensions. ρ is called resistivity.

Resistance:

• It is defined as the hurdles in the path of flow of current.
• The SI unit of resistance is the ohm.
• It is denoted by the symbol Ω.
• It depends on the material of the conductor and the dimensions of the conductor.
• In other words, we can say it is the ratio of voltage to the current.
• R= (rho×length)/area
• Note: rho=Resistivity.

The correct answer is Free Electrons.

Key Points

• Current carriers in solid conductors are Free Electrons.
  • In solid conductors (e.g. metals), there are a large number of free electrons.
  • When an electric field (i.e. PD) is applied to the conductor, the free electrons start drifting in a particular direction to constitute that current.

Additional Information

• Some liquids are conductors of electricity.
  • A Conducting liquid is called an electrolyte (e.g. solution of CuSO₄).
  • In conducting liquids, ions (positive and negative) are the current carriers.
• Under ordinary conditions, gases are insulators.
  • However, when a gas under low pressure is subjected to a high electric field (i.e. high p.d.), Ionisation of in gases molecules takes place, i.e. electrons and positive ions are formed.
• Hence, current carriers in gases are free electrons and positive ions.

Lightning:

The visible discharge of electricity occurs when a region of a cloud acquires an excess electrical charge (either positive or negative) that is sufficient to break down the resistance of air.

Current is a measure of the flow of electric charge over time.

It is defined as   \(I = \frac{{dq}}{{dt}}\)

where q = Charge

t = Time

I = Current

Calculation:

Given:

q = 25 C

I = 2.5 kA

\(I = \frac{{dq}}{{dt}}\)

\(2500 = \frac{{25}}{{ t}}\)

t = 10 milliseconds

Concept:

The magnitude of the force between the conductor is given by

\(F = \frac{\mu_{0}I_{1}I_{2}l}{2\pi d} = 2 \times 10^{-7} \times \frac{I_{1}I_{2}l}{d} \)

Where;

I_1,2 → current carried by the conductors 

l → Length

d→ Distance between conductors

Calculation:

Given;

I1,2 → current carried by the conductors = 20 A

d→ Distance between conductors = 20 cm = 0.2 m

Then;

The magnitude of the force per meter between the conductor is given by;

\(\frac{F}{l} = \frac{\mu_{0}I_{1}I_{2}}{2\pi d} = 2 \times 10^{-7} \times \frac{I_{1}I_{2}}{d}= 2 \times 10^{-7} \times \frac{20 \times 20}{0.2}=4 \times 10^{-4} \, N\)

Additional Information

Concept of Current Density:

Ohms’ law: At constant temperature, the current through a resistance is directly proportional to the potential difference across the resistance.

V = R I

Where V is the potential difference, R is resistance and I is current flowing

Current density (J): The electric current per unit area is called current density.

\(Current~density~\left( J \right)=\frac{Current~\left( I \right)}{Area~\left( A \right)}\)

Conductivity (σ): The property of a conductor due to which the current flows through it is called the conductivity of that conductor.

\(Resistance~\left( R \right)=\frac{\rho ~l}{A}\)

Where ρ is resistivity = 1/σ, l is the length and A is the area of the conductor

As, V = R I 

\(Resistance~\left( R \right)=\frac{\rho ~l}{A}\)

\(V=\frac{\rho ~l}{A}\times I=\left( \frac{1}{σ } \right)\times l\times \frac{I}{A}=\left( \frac{1}{σ } \right)\times l\times J\)

\(J=σ \times \frac{V}{l}=σ ~E\)

σ = J/E

Superconductivity: It is the state of the material in which its resistance becomes zero as well as it behaves as perfect diamagnetic when its temperature is reduced below transition temperature Tc and the magnetic field is less than the critical magnetic field Hc.

The current density of the superconductor depends on critical magnetic field strength and temperature.

Superconductors are divided into two types based on magnetic properties:

1) Type-I or Ideal or soft superconductor

2) Type-I or Hard superconductor.

Type-I Superconductor:

A superconducting state is completely diamagnetic up to a certain critical magnetic field (Hc). Above Hc, the superconducting state changes it’s behavior and undergoes to normal state abruptly.

This is explained with the help of the following curve:

Type-II Superconductor:

• It loses their superconductivity gradually because they are made-up by a combination of Hard metal and alloys that show different magnetization behavior.
• It shows superconductivity up to a lower critical magnetic field Hc1 and beyond this, the magnetization changes gradually and reaches zero at upper critical magnetic field Hc2 and due to this, it is useful in the preparation of high-field electromagnets.

Important Points:

Characteristics of superconductors in comparison to a normal metal is as shown:

Concept:

Current passing through the conductor, I = q/t = ne / t

Where

n = number of electrons 

e = charge of electron

t = time duration

Calculation:

q = e = 1.62 × 10-19 

t = 1 sec

⇒ I = n × 1.62 × 10-19

⇒ 8 = n × 1.62 × 10-19

⇒ n = 4.93 × 1019 ≈ 5 × 1019

Concept:

The boundary condition for electrostatic fields are defined as:

E1t = E2t (Tangential components are equal across the boundary surface)

Also, the normal component satisfies the following relation:

D1n – D2n = ρs

For a charge-free boundary, ρs = 0, the above expression becomes:

D1n – D2n = 0

D1n = D2n

Calculation:

As Tangential components are equal across the boundary surface

E₁t = E2t  

E1t = 10 Vm-1

so tangential component of the electric field on the other side is:

E2t = 10 Vm-1

Explanation

Conduction current density:

• It is defined as the amount of current or charges that flow through the conduction surface within a time 't'.
• The current carried by conductors due to the flow of charges is called conduction current.
• The conduction current follows Ohm's Law
• It is given by: J_C = σE 

where J_C = Conduction current density

σ = Conductivity

E = Electric field

Displacement current density:

• It is defined as the rate of change of the electric displacement field with respect to time 't'.
• The current due to changing electric field is called displacement current.
• The displacement current does not follow Ohm's Law.
• It is given by: J_D = \( {\epsilon_o}{dE \over dt}\)

where J_D = Displacement current density

Superconductivity: It is the state of the material in which its resistance becomes zero as well as it behaves as perfect diamagnetic when its temperature is reduced below transition temperature Tc and the magnetic field is less than the critical magnetic field Hc.

Superconductors ripple magnetic field, hence they are creating regions free from magnetic field. 

The current density of the superconductor depends on critical magnetic field strength and temperature.

Superconductors are divided into two types based on magnetic properties:

1) Type-I or Ideal or soft superconductor

2) Type-I or Hard superconductor.

Type-I Superconductor:

A superconducting state is completely diamagnetic up to a certain critical magnetic field (Hc). Above Hc, the superconducting state changes it’s behavior and undergoes to normal state abruptly.

This is explained with the help of the following curve:

Type-II Superconductor:

• It loses their superconductivity gradually because they are made-up by a combination of Hard metal and alloys that show different magnetization behavior.
• It shows superconductivity up to a lower critical magnetic field Hc1 and beyond this, the magnetization changes gradually and reaches zero at upper critical magnetic field Hc2 and due to this, it is useful in the preparation of high-field electromagnets.

Important Points:

Characteristics of superconductors in comparison to a normal metal is as shown: