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Magnetic Field due to a Current Element Physics Moving Charges and Magnetism Physics Class 12th

A very long conducting wire is bent in a semi-circular shape from A to B as shown in figure. The magnetic field at point P for steady current configuration is given by:

Option 1 -

$\frac{μ_{0} i}{4 R} [1 - \frac{2}{π}]$ pointed into the page

Option 2 -

$\frac{μ_{0} i}{4 R}$ pointed into the page

Option 3 -

$\frac{μ_{0} i}{4 R}$ pointed away from the page

Option 4 -

$\frac{μ_{0} i}{4 R} [1 - \frac{2}{π}]$ pointed away from page

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Answered by

Raj Pandey | Contributor-Level 9

a month ago

Correct Option - 4

Detailed Solution:

${\overset{?}{B}}_{P} = {\overset{?}{B}}_{upper wire} \otimes + {\overset{?}{B}}_{semi-circle} ? + {\overset{?}{B}}_{lower-wire} \otimes$

$B_{P} = - \frac{μ_{0} i}{4 π R} + \frac{μ_{0} i}{4 R} - \frac{μ_{0} i}{4 π R} = \frac{μ_{0} i}{4 R} (1 - \frac{2}{π})$ pointing away from the page

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A very long conducting wire is bent in a semi-circular shape from A to B as shown in figure. The magnetic field at point P for steady current configuration is given by:

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