Question

Which of the following in electricity is analogous to momentum $mv$ in dynamics?
(I is current, V is voltage, L is inductance and Q is charge)
A. IV
B. IL
C. QL
D. IQ

Answer 1

Hint: To solve the given problem make use of the Lenz law. The Lenz law says that the potential difference across an inductor is equal to the product of its inductance and the rate of change in current in the inductor. Then compare the equation with equation of force from Newton’s second law of motion.

Complete step by step answer:
Let us first understand a law called Lenz law for electromagnetism. The Lenz law says that the potential difference across an inductor is equal to the product of its inductance and the rate of change in current in the inductor. If the inductance of the inductor is L and the current flowing in it is I, then the potential difference across the inductor is given as $V=L\dfrac{dI}{dt}$ ….. (i),
where $\dfrac{dI}{dt}$ is the rate of change in the current in the inductor.
For a given inductor, the value of its inductance is constant. Therefore, we can write the equation (i) as $V=\dfrac{d(LI)}{dt}$ ….. (ii)
Now, let us compare this equation with Newton’s second law of motion, which says that the force on a body is equal to the rate of change in momentum of the body.
i.e. $F=\dfrac{dP}{dt}$, where F is force and P is momentum.
Momentum of a body is given as,
$P=mv$, where m and v are the mass and velocity of the body.
Then, this means that $F=\dfrac{d(mv)}{dt}$ ….. (iv).
Now, we can see that equations (iii) and (iv) look similar. Therefore, we can say that potential difference is analogous to force and momentum (mv) is analogous to product of inductance and current (IL).

Hence, the correct option is B.

Note: Do not confuse the term analogous. It is not of much importance. It is simply used to show that we can treat potential difference across an inductor as that of force in dynamics. It is used only to make students understand things. It does not mean that the quantities are related.