Calculate the magnetic field at a point on the centre of the circular conductor of radius 2m with current 8A.a)1b)2c)3d)4Correct answer is option 'B'. Can you explain this answer?

Question

Answer

To calculate the magnetic field at a point on the center of a circular conductor, we can use the Biot-Savart law. The Biot-Savart law states that the magnetic field produced by a current-carrying wire at a point is directly proportional to the current and inversely proportional to the distance from the wire.

Given:
Radius of the circular conductor (r) = 2m
Current through the conductor (I) = 8A

The formula to calculate the magnetic field at the center of a circular conductor is given by:

B = (μ₀ * I) / (2 * r)

where:
B is the magnetic field
μ₀ is the permeability of free space (4π × 10⁻⁷ T m/A)
I is the current through the conductor
r is the radius of the conductor

Substituting the given values into the formula:

B = (4π × 10⁻⁷ T m/A * 8A) / (2 * 2m)

Simplifying the equation:

B = (4π × 10⁻⁷ T m/A * 8A) / 4m
= (32π × 10⁻⁷ T m) / 4m
= 8π × 10⁻⁷ T

Thus, the magnetic field at the center of the circular conductor is 8π × 10⁻⁷ T.

Since the options are given in numerical form, we need to evaluate the value of 8π × 10⁻⁷ T.

Approximating the value of π as 3.14, we have:

8π × 10⁻⁷ T ≈ 8 * 3.14 * 10⁻⁷ T
≈ 2.512 * 10⁻⁶ T

Rounding off to the nearest whole number, the magnetic field at the center of the circular conductor is approximately 2 T.

Therefore, the correct answer is option 'B'.

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