Question

The magnetic flux near the axis and inside the air core solenoid of length 60 cm carrying current 'I' is 1.57 × 10^-6 Wb. Its magnetic moment will be ______.

(cross-sectional area is very small as compared to length of solenoid, µ₀ = 4π × 10^-7 SI unit)

Options

• 0.50 A

• 0.75 A

• 0.25 A

• 1 A

Answer 1

The magnetic flux near the axis and inside the air core solenoid of length 60 cm carrying current 'I' is 1.57 × 10^-6 Wb. Its magnetic moment will be 0.75 A.

(cross-sectional area is very small as compared to length of solenoid, µ₀ = 4π × 10^-7 SI unit) 

Explanation:

For a solenoid magnetic field inside is given by

`"B" = (mu_0 "NI")/"L"  "where N is the total number of turns"`

`"B" = phi/"A"  "where A is the area"`

`therefore phi/"A" = (mu_0 "NI")/"L"`

`therefore phi = (mu_0 "NIA")/"L" = (mu_0 "M")/"L"`

where M = NIA = magnetic moment

`therefore "M" = (phi  "L")/mu_0`

`= (1.57 xx 10^-6 xx 0.6)/(4pi xx 10^-7)`

`= 0.75  "AM"^2`