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,

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

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,

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

Cancelling π on both numerator and denominator,

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

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.

Answer 2

$\large \bigstar \bf {\underbrace{ \color{navy}{ \: \: \: \: \: \: \: \: \: \: given \: \: \: \: \: \: \: \: \: \: \: }} }\bigstar$

• Magnetic field = 16 T
• Distance = 2.4 cm

$\large \bigstar \bf {\underbrace{ \color{navy}{ \: \: \: \: \: \: \: \: \: \: To find \: \: \: \: \: \: \: \: \: \: \: }} }\bigstar$

• Current through the wire = ?

$\large \bigstar \bf {\underbrace{ \color{navy}{ \: \: \: \: \: \: \: \: \: \: Formula \: \: \: \: \: \: \: \: \: \: \: }} }\bigstar$

• $\large \bigstar \mid\sf \overline {\color{red}\boxed{ \: \: \: \: \: \: \: b = \frac{ \mu_{0} \: l }{2\pi \: r \: \: } \: \: \: \: \: \: }} \mid \bigstar$

$\large \bigstar \bf {\underbrace{ \color{navy}{ \: \: \: \: \: \: \: \: \: \: Note \: \: \: \: \: \: \: \: \: \: \: }} }\bigstar$

Here,

• B is the magnetic field
• I is the current
• r is the distance
• $\mu \:o$ is the magnetic constant

$\large \bigstar \bf {\underbrace{ \color{navy}{ \: \: \: \: \: \: \: \: \: \: here \: \: \: \: \: \: \: \: \: \: \: }} }\bigstar$

$\\ \bf \red B = 10 { }^{ - 6} \\ \bf \red l = ? \\ \bf \red r = 2.4 \\ \bf \red {\mu _{0}} = 4\pi \times 10 {}^{ - 7}$

$\large \bigstar \bf {\underbrace{ \color{navy}{ \: \: \: \: \: \: \: \: \: \: Solution \: \: \: \: \: \: \: \: \: \: \: }} }\bigstar$

$\begin{gathered}I=\dfrac{2\pi rB}{\mu_o}\\\\I=\dfrac{2\pi \times 2.4\times 10^{-2}\times 16\times 10^{-6}}{4\pi \times 10^{-7}}\\\\I=1.92\ A\end{gathered}$

So, the current of 1.92 A is flowing through the wire. Hence, this is the required solution.

$\large \bigstar \bf {\underbrace{ \color{navy}{ \: \: \: \: \: \: \: \: \: \: additional\: information \: \: \: \: \: \: \: \: \: \: \: }} }\bigstar$

1. Magnetic Field is the region around a magnetic material or a moving electric charge within which the force of magnetism acts.
2. A magnetic field can be illustrated in two different ways.

• Magnetic Field Vector
• Magnetic Field Lines