(a) V = RI
(b) J = E/ρ
(c) 
(d) R = ρL/A
Correct Answer: (c)
Explanation
Current density is proportional to electric field.
Notes for
More Information
CONCEPT: Ohm’s Law
1. Ohm’s law states
that at constant temperature, the potential difference (V) across
a current-carrying conductor is directly proportional to
the current (I) flowing through it.
2. Mathematically:
3. Hence,
4. Where:
·
= potential difference
(volt)
·
= current (ampere)
·
= resistance (ohm)
5. Metallic
conductors generally obey Ohm’s law under normal physical conditions.
Ohm’s Law in Point Form / Vector
Form
6. In electromagnetics
and material science, Ohm’s law is expressed in vector (point) form.
7. This form
relates current density and electric field.
8. The vector
(point) form of Ohm’s law is:
9. Where:
·
= current density (A/m²)
·
= electric field intensity
(V/m)
·
= electrical conductivity
(S/m)
Important Relation
10.
Conductivity (σ) is the reciprocal
of resistivity (ρ):
EXPLANATION
11.
In a conducting material, the applied electric field (E) causes
charge carriers to drift.
12.
This drift produces current density (J).
13.
The proportionality constant between 
and 
is the conductivity
(σ).
14.
Therefore, Ohm’s law in point or vector form is given
by:
Final Conclusion
15.
Scalar form of Ohm’s law:
16.
Vector (point) form of Ohm’s law:
17.
The vector form is mainly used for continuous media, fields, and
material analysis.
✔️ Key Exam
Line
Ohm’s law in point (vector) form
is: