Question

(26. A long solenoid with 40 turns per centimeter carries
a current of 1 A. The magnetic energy stored per
unit volume is
(1) 1.6 J/m3
(2) 321 J/m3
(3) 3.21 J/m3
(4) 6.41 J/m3​

Answer 1

Answer:

Explanation:

Given A long solenoid with 40 turns per centimeter carries

a current of 1 A. The magnetic energy stored per

unit volume is

We know that  n = 40 turns / cm = 4 x 10^3  / m

B = μo nI

So energy per unit volume = 1/2μo B^2

                                          = 1/2μo ( μo nI)^2

                                        = μo n^2 I^2 / 2

                                          = 4π x 10^-7 x (4 x 10^3)^2 x 1^2 / 2

                                         = 32 π x 10^-1

                                         = 3.2 π J /  m^3

                                          = 10.048 J / m^3

Answer 2

(3) 3.21 J/m^3

Explanation:

It is given in the question that:

n/l = 40/cm = (40/cm) (100cm/m) = 4000/m

We know that:

Energy per unit volume = (1/2μ0)B^2

Energy per unit volume = (1/2μ0) (μ0nI)^2 = μ0 n^2 I^2/2

Now by putting values in this expression:

Energy per unit volume = E/V = 3.21 J/m^3