TS EAMCET · Physics · Electromagnetic Waves

A small cube of side of $1 mm$ is placed at the center of a circular loop of radius, $20 cm$ . If the current in the loop is, $2 A$ then the magnetic energy stored inside the cube is (Assume $μ_{0} = 4 π \times 10^{- 7}$ SI units )

A $1.57 \times 10^{- 18} J$
B $2.57 \times 10^{- 14} J$
C $1.57 \times 10^{- 14} J$
D $4.57 \times 10^{- 13} J$

Verified Solution

Answer & Solution

Correct Answer

(C) $1.57 \times 10^{- 14} J$

Step-by-step Solution

Detailed explanation

The formula of energy density in terms of strength of the magnetic field is, ud=12×B2μ0, then the energy of stored will be, u=ud×V=12×B2μ0×V, here the strength of the magnetic field can be calculated from the formula, B=μ0i2r,…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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A small cube of side of 1 mm is placed at the center of a circular loop of radius, 20 cm. If the current in the loop is, 2 A then the magnetic energy stored inside the cube is (Assume μ0=4π×10-7 SI units )

Step-by-step Solution

A small cube of side of $1 mm$ is placed at the center of a circular loop of radius, $20 cm$ . If the current in the loop is, $2 A$ then the magnetic energy stored inside the cube is (Assume $μ_{0} = 4 π \times 10^{- 7}$ SI units )