A circular loop of radius 0.0157 m carries a current of 2 A. The magnetic field at the centre of the loop isa)3.14 x 10-5weber /m2b)1.57 x 10-5weber /m2c)1.57 x 10-5weber /m2d)8.0 x 10-5weber /m2Correct answer is option 'D'. Can you explain this answer?

Question

A circular loop of radius 0.0157 m carries a current of 2 A. The magnetic field at the centre of the loop is&#8203;a)3.14 x 10-5weber /m2b)1.57 x 10-5weber /m2c)1.57 x 10-5weber /m2d)8.0 x 10-5weber /m2Correct answer is option 'D'. Can you explain this answer?

Answer

The magnetic field due to a circular loop is given by:
B= μ₀2πi/4πr
=10⁻⁷×2π×2/0.0157
=8×10⁻⁵ Wb/m²

Answer

Answer

For a circular loop, B= ([u(not) /4*pie] *2*pie*I)/r Where u(not) /4 pie=10^-7....ı=2a...r=.0157 Solving it we get 8*10^-5 tesla Hope u get it!

Answer

To find the magnetic field at the center of a circular loop carrying a current, we can use Ampere's law. Ampere's law relates the magnetic field around a closed loop to the current passing through the loop.

Ampere's Law:
Ampere's law states that the line integral of the magnetic field (B) around a closed loop is equal to the product of the current enclosed by the loop (I) and the permeability of free space (μ₀).

∮ B · dl = μ₀I

where ∮ represents the line integral around the loop, B is the magnetic field, dl is an infinitesimal element of the loop, I is the current, and μ₀ is the permeability of free space (μ₀ = 4π × 10⁻⁷ Tm/A).

Applying Ampere's Law:
In this case, the circular loop has a radius of 0.0157 m and carries a current of 2 A. We want to find the magnetic field at the center of the loop.

Since the loop is symmetric, we can choose a circular path of radius r within the loop. The line integral of the magnetic field around this path is given by:

∮ B · dl = B ∮ dl = B(2πr)

Here, B is the magnetic field at the center of the loop and ∮ dl represents the circumference of the chosen circular path.

Since the current is enclosed by the chosen circular path, we can apply Ampere's law:

B(2πr) = μ₀I

Solving for B:
Substituting the given values, we have:

B(2π(0.0157)) = (4π × 10⁻⁷)(2)

Simplifying the equation, we find:

B = (4π × 10⁻⁷)(2) / (2π(0.0157))

B = (4π × 10⁻⁷) / (0.0157)

B ≈ 8.0 × 10⁻⁵ T

Therefore, the magnetic field at the center of the loop is approximately 8.0 × 10⁻⁵ T, which is equivalent to 8.0 × 10⁻⁵ Weber/m².

Hence, the correct answer is option 'D' (8.0 × 10⁻⁵ Weber/m²).

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