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The magnetic field inside a solenoid is 1.52T. The solenoid has an inner diameter of 3.08cm and a length of 29.1cm. Calculate the magnetic energy density in the field (unit in ×10⁶Jm⁻³).

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Final answer:

To calculate the magnetic energy density inside a solenoid, use the formula u = B^2 / (2μ0). For a magnetic field strength of 1.52 T, the energy density is approximately 9.186 x 10^6 J/m^3 or 9.186 MJ/m^3.

Step-by-step explanation:

To calculate the magnetic energy density in the field of a solenoid, we use the formula for the energy density u in a magnetic field, which is given by:

u = B2 / (2μ0)

where B is the magnetic field strength inside the solenoid, and μ0 is the vacuum permeability constant, which has a value of 4π x 10-7 T·m/A (tesla meter per ampere).

In this problem, we are given the magnetic field strength B as 1.52 T. Plugging this into the formula yields:

u = (1.522) / (2 x 4π x 10-7)

u = 2.3104 / (8π x 10-7)

u = 2.3104 / (25.1327412287 x 10-7)

u = 9.186 x 106 J/m3

The magnetic energy density in the solenoid field is therefore approximately 9.186 x 106 J/m3, which can also be expressed as 9.186 MJ/m3.

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