Question

A solenoid with n1 = 1200 turns/m and a current I1 = 2.5 A is filled with a paramagnetic material at a temperature T1 = 320 K. A second solenoid with n2 = 1000 turns/m and a current I2= 0.85 A is filled with the same paramagnetic material at a different temperature T2. The magnetizations are the same in both cases. What is the value of T2?

Answer 1

Answer:

$T_2$ = $90.667K$

Explanation:

Given:

For the first solenoid

Number of turns, n₁ = 1200 turns/m

Current, I₁ = 2.5 A

Paramagnetic material temperature, T₁ = 320 K

Now for the second solenoid

Number of turns, n₂ = 1000 turns/m

Current, I₂ = 0.85 A

Paramagnetic material temperature = T₂

The magnetic flux (B) is given as

$B=\frac{c\mu_onI}{T}$

where,

c = curie's constant

μ₀ = arithmetic constant

also it is given that the magnetization in both the cases are same

therefore the magnetic flux will also be equal

thus,

$\frac{c\mu_on_1I_1}{T_1}$ = $\frac{c\mu_on_2I_2}{T_2}$

or

$\frac{n_1I_1}{T_1}$ = $\frac{n_2I_2}{T_2}$

or

$\frac{1200\times 2.5}{320}$ = $\frac{1000\times 0.85}{T_2}$

or

$9.375$ = $\frac{850}{T_2}$

or

$T_2$ = $\frac{850}{9.375}$

or

$T_2$ = $90.667K$