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QJEEM19Phfe38: JEE Main 2019 Physics - Class 12 JEEM19Phfe38 Solution: A current loop, having two circular arcs joined by two radial…

A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a current of 10 A. The magnetic field at point O will be close to :

JEE Main 2019 (Online) 9th January Morning Slot Physics - Magnetic Effect of Current Question 168 English

Multiple Choice Options

  • A 1.0 ×\times 10 −- 7 T
  • B 1.5 ×\times 10 −- 7 T
  • C 1.5 ×\times 10 −- 5 T
  • D 1.0 ×\times 10 −- 5 T

Step-by-Step Verified Solution

Magnetic field due to circular arc

B→=μ0 i θ4πr\overrightarrow B = {{{\mu _0}\,i\,\theta } \over {4\pi r}}

Due to QR arc magnetic field is outward direction of the plane.

And due to PS arc magnetic field is inward direction of the plane,

So, net magnetic field,

B→=(B→QR−B→PS)K^\overrightarrow B = \left( {{{\overrightarrow B }_{QR}} - {{\overrightarrow B }_{PS}}} \right)\widehat K

B→=μ0iθ4π(13×10−2−15×10−2)K^\overrightarrow B = {{{\mu _0}i\theta } \over {4\pi }}\left( {{1 \over {3 \times {{10}^{ - 2}}}} - {1 \over {5 \times {{10}^{ - 2}}}}} \right)\widehat K

B→=10−7×10×π4(13×10−2−15×10−2)K^\overrightarrow B = {10^{ - 7}} \times 10 \times {\pi \over 4}\left( {{1 \over {3 \times {{10}^{ - 2}}}} - {1 \over {5 \times {{10}^{ - 2}}}}} \right)\widehat K

∣B→∣=1×10−5  T\left| {\overrightarrow B } \right| = 1 \times {10^{ - 5}}\,\,T

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