A long solenoid with 40 turns per cm carries a current of 1A. The magnetic energy stored per unit volume is __________`J//m^(3)`

Options

A. `3.2pi`
B. `32Pi`
C. `1.6pi`
D. `6.4pi`

Answer

a

Explanation

n= 40turns /cm = 4000 turns/m I=1A
`B= munI`
Magnetic energy per unit volume
`U_(b) = (1)/(2)(B^(2))/(mu_(0)) = (1)/(2)(mu_(0)nI^(2))/(mu_(0))= (mu_(0)n^(2)I^(2))/(2)`
`=2pixx10^(-7)xx(4xx10^(3))^(2)xx1^(2)`
`= 2pixx16xx10^(-7+6)= 3.2pijm^(-3)`