Find the current density of a material with resistivity 20 units and electric field intensity 2000 units.a)400b)300c)200d)100Correct answer is option 'D'. Can you explain this answer?

Question

Accepted Answer

Answer: d
Explanation: The current density is given by J = σ E, where σ is the conductivity. Thus resistivity ρ = 1/σ. J = E/ρ = 2000/20 = 100 units.

Answer

Given data:
- Resistivity (ρ) = 20 units
- Electric field intensity (E) = 2000 units

Formula:
The current density (J) can be calculated using the formula:
J = σ * E

Explanation:

1. Resistivity:
Resistivity (ρ) is a measure of how strongly a material opposes the flow of electric current. It is denoted by the symbol ρ and is measured in ohm-meters.

2. Electric Field Intensity:
Electric field intensity (E) is a vector quantity that describes the strength of an electric field at a given point. It is measured in units of volts per meter (V/m).

3. Current Density:
Current density (J) is the amount of current flowing through a unit area of a material. It is a vector quantity and is denoted by the symbol J. The unit of current density is amperes per square meter (A/m^2).

Calculation:
Given resistivity (ρ) = 20 units and electric field intensity (E) = 2000 units
We know that conductivity (σ) = 1/ρ
So, conductivity (σ) = 1/20 = 0.05
Now, substitute the values of σ and E into the formula:
J = σ * E
J = 0.05 * 2000
J = 100 A/m^2
Therefore, the current density of the material is 100 A/m^2, which corresponds to option 'D'.

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