First slide

Magnetic field due to a straight current carrying wire

Question

Equal currents i = 1 A are flowing through the wires parallel toy-axis located at x = +1 m, x = +2 m, x = +4 m etc. but in opposite directions as shown. The magnetic field at origin (in T) would be

Difficult

A

$- 1 .33 \times 10^{7} \hat{k}$
B

$1 .33 \times 10^{- 7} \hat{k}$
C

$2 .67 \times 10^{- 7} \hat{k}$
D

$- 2 .67 \times 10^{- 7} \hat{k}$

Solution

$\begin{array}{l} \vec{B} = \frac{μ_{0}}{2 π} [(\frac{1}{1} + \frac{1}{4} + \frac{1}{16} +) \hat{k} - (\frac{1}{2} + \frac{1}{8} + . ..) \hat{k}] \\ = \frac{μ_{0}}{2 π} [(\frac{1}{1 - \frac{1}{2}}) \hat{k} - \frac{1}{2} (\frac{1}{1 - \frac{1}{4}}) \hat{k}] \\ = \frac{2}{3} \frac{μ_{0}}{2 π} \hat{k} \\ = (\frac{2}{3} \times 2 \times 10^{- 7}) \hat{k} \\ = 1 .33 \times 10^{- 7} \hat{k} \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App