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

`T_2` =
`90.667K`

Step-by-step 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=(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,

`(c\mu_on_1I_1)/(T_1)` =
`(c\mu_on_2I_2)/(T_2)`

or

`(n_1I_1)/(T_1)` =
`(n_2I_2)/(T_2)`

or

`(1200* 2.5)/(320)` =
`(1000* 0.85)/(T_2)`

or

`9.375` =
`(850)/(T_2)`

or

`T_2` =
`(850)/(9.375)`

or

`T_2` =
`90.667K`