Question

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

Answer 1

Hint: The dimension of electric field vector (E) is volt/meter and the dimension of magnetic field vector (H) is Ampere/meter. In the given question, we can use these dimensions of electric field factor (E) and magnetic field vector (H) to find the answer. Volt is the dimension of voltage and ampere is the dimension of current.

Complete step by step answer: The dimension of electric field vector (E) is volt/meter and the dimension of magnetic field vector (H) is Ampere/meter.
Therefore, the ratio of electric field vector and magnetic field vector is given as,
$\dfrac{E}{H} = \dfrac{{\dfrac{{volt}}{{meter}}}}{{\dfrac{{ampere}}{{meter}}}} = \dfrac{{volt}}{{ampere}}$
Thus, the ratio of electric field vector and magnetic field vector is volt/ampere.
Volt is the dimension of voltage and ampere is the dimension of current. Therefore, the ratio of electric field vector E and magnetic field vector H becomes voltage/current $\left( {\dfrac{V}{I}} \right)$
Now, according to Ohm’s law, voltage/current ($\left( {\dfrac{V}{I}} \right)$) is equal to the resistance.
Thus, $\left( {\dfrac{E}{H}} \right)$ has the dimensions of resistance.
Hence, option (A) is the correct option.

Note: In this question you are asked to find the ratio of electric field vector E and magnetic field vector H. To evaluate the given question student must remember the dimensions of the electric field vector and magnetic field vector, then after substituting these terms in the $\dfrac{E}{H}$ equation, we will get our desire result that is resistance.