Question

Magnetic field at a distance 2.4 cm from a long straight wire is 16T. What must be

current through the wire?​

Answer 1

Answer:

Current = 1.92 × 10⁶ A

Explanation:

Given:

Magnetic field = 16 T

Distance = 2.4 cm = 0.024 m

To Find:

Current through the wire

Solution:

Here we have to find the current passing through the wire.

Magnetic field due to a long straigt current carrying wire is given by,

\boxed{\sf B =\dfrac{\mu_0\:I}{2\pi\:r}}

B=

2πr

μ

0

I

where B is the magnetic field,

I is the current flowing through the wire,

r is the distance,

μ₀ is the magnetic constant = 4 π × 10⁻⁷ H/m

Substituting the data we get,

\sf \dfrac{4\pi\times 10^{-7}\times I}{2\pi \times 0.024} =16

2π×0.024

4π×10

−7

×I

=16

Cancelling π on both numerator and denominator,

\sf \dfrac{2\times 10^{-7}\times I}{ 0.024} =16

0.024

2×10

−7

×I

=16

2 × 10⁻⁷ × I = 16 × 0.024

2 × 10⁻⁷ × I = 0.384

I = 0.384/2 × 10⁻⁷

I = 0.192 × 10⁷

I = 1.92 × 10⁶ A

Hence the current flowing through the wire is 1.92 × 10⁶ A.