Question 42

A small cube of side 1 mm is placed at the centre of a circular loop of radius 10 cm carrying a current of 2 A. The magnetic energy stored inside the cube is $$\alpha \times 10^{-14}$$ J. The value of $$\alpha$$ is _______.
$$(\mu_0 = 4\pi \times 10^{-7}$$ Tm/A, $$\pi = 3.14)$$

$$B = \frac{\mu_0 I}{2R}$$

$$u_B = \frac{B^2}{2\mu_0}$$

$$U = u_B \cdot V = \frac{B^2}{2\mu_0} \cdot V$$

$$B = \frac{(4\pi \times 10^{-7}) \times 2}{2 \times 0.1} = \frac{4\pi \times 10^{-7}}{0.1} = 4\pi \times 10^{-6} \text{ T}$$

$$U = \frac{(4\pi \times 10^{-6})^2}{2 \times (4\pi \times 10^{-7})} \times 10^{-9}$$

$$U = 2 \times 3.14 \times 10^{-14} = 6.28 \times 10^{-14} \text{ J}$$

$$\alpha = 6.28$$

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A small cube of side 1 mm is placed at the centre of a circular loop of radius 10 cm carrying a current of 2 A. The magnetic energy stored inside the cube is $$\alpha \times 10^{-14}$$ J. The value of $$\alpha$$ is _______.$$(\mu_0 = 4\pi \times 10^{-7}$$ Tm/A, $$\pi = 3.14)$$