Question

The ratio of electric field vector ${\text{E}}$ and magnetic field vector ${\text{H}}$ i.e., $\left( {\dfrac{{\text{E}}}{{\text{H}}}} \right)$ has the dimensions of:
(A) Resistance
(B) Inductance
(C) Capacitance
(D) Product of inductance and capacitance

Answer 1

Hint: For finding the ratio of the dimensions of electric field vector and magnetic field vector, first of all try to recall the definition of electric field vector and its formula. Then find out the SI unit of the electric field vector. Similarly with magnetic field vectors. Then find the ratio of both quantities.

Complete solution:
Electric field is a region or space around a charged body in which its influence can be experienced. Electric field intensity is the measure of strength of the electric field and it is defined as the force experienced per unit test charge. It is a vector quantity.
Formula for electric field intensity is given by
${{\vec E = }}\dfrac{{{{\vec F}}}}{{{{\text{q}}_{\text{0}}}}}$
The SI unit of force is newton represented by ${\text{N}}$.
The SI unit of charge is coulomb represented by ${\text{C}}$.
The SI unit of the electric field vector is ${\text{N/C}}$ or ${\text{V/m}}$.
Magnetic field is a region or space around a magnet (or a current carrying conductor) in which its influence can be experienced. Magnetic field vector is defined as the ampere turn per unit length of the solenoid.
The SI unit of magnetic field vector is ${\text{A/m}}$.
The dimensions of the electric field vector is ${\text{volt/metre}}$ represented by ${\text{V/m}}$. The dimensions of the magnetic field vector is ${\text{Ampere/metre}}$ represented by ${\text{A/m}}$.
The ratio of dimensions of electric field vector and magnetic field vector is $\dfrac{{\dfrac{{\text{V}}}{{\text{m}}}}}{{\dfrac{{\text{A}}}{{\text{m}}}}}$ or $\dfrac{{\text{V}}}{{\text{A}}}$.
But according to the ohm’s law, the ratio of voltage and current gives resistance.

Therefore, option (A) is the correct choice.

Note: According to the ohm’s law the current (I) flowing through a conductor is directly proportional to the potential difference (V) applied across the ends of the conductor provided that physical conditions like temperature, pressure of conductor remain the same. Formula: ${\text{V = IR}}$ where ${\text{I = }}$ current flowing through the conductor and ${\text{R = }}$ resistance of conductor.