Question

If the peak value of magnetic field of a beam is 12 × 10–8T. Then, its average energy density is


(a) 12 × 10–10 W/m2

(b) 5.37 × 10–9 W/m2

(c) 4.2 × 10–9 W/m2

(d) 1.8 × 10–6 W/m2​

Answer 1

Answer:

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Answer 2

Given info : If the peak value of magnetic field of a beam is 12 × 10^-8 T.

To find : Its average energy density is ...

solution : Let's derive the formula of energy density.

energy density = total energy stored/volume

total energy stored = work done by inductor , W = 1/2 Li²

and volume = Area × length = Al

so energy density = 1/2 Li²/Al ....(1)

we know, magnetic flux due to inductor = Li = NBA ....(2)

magnetic field for circular inductor, B = μ₀Ni/l

⇒i = Bl/μ₀N ...(3)

now putting equations (2) and (3) in (1), we get,

energy density = B²/2μ₀ , this is remarkable formula to find energy density if peak value of magnetic field is given.

here, B = 12 × 10^-8 T

so, energy density = (12 × 10^-8)²/(2 × 4π × 10^-7)

= 144/8π × 10^-9 W/m²

= 5.73 × 10^-9 W/m²

Therefore the energy density is 5.73 × 10^-9 W/m²