Question

At which temperature the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at 47°C?

पर्याय

• 80 K

• −73 K

• 4 K

• 20 K

Answer 1

20 K

Explanation:

The magnetic force per unit length (f) between two parallel long straight wires separated by a distance d is given by:

f = `(mu_0 I_1 I_2)/(2 pi d)`

In this rectangular loop, the wires PQ and RS are parallel, and both carry the same current (which is the current I measured by the ammeter).

Since the dimensions of the loop (the distance d = PR = 5 cm) and the medium remain constant, the force per unit length depends only on the product of the currents:

f ∝ I²

Case 1: The current is I. The force is f₁ ∝ I².

Case 2: The current is 2I. The force is f₂ ∝ (2I)² = 4I².

To find the ratio:

`(f_(PQ)^I)/(f_(PQ)^(2I)) = I^2/(4I^2)`

= `1/4`

∴ The ratio of magnetic forces per unit length is 1 : 4.