KVPY SX SB Exam 2016 Question Paper

Question : 93 of 120

Marks: +1, -0

Two infinitely long wires each carrying current I along the same direction are made into the geometry as shown in the figure. The magnetic field at the point P is

${µ_0I}/{πr}$
${µ_0I}/r(1/π+1/4)$
Zero
${µ_0I}/{2πr}$

Validate

Solution:

(B↖{→})_{ 0 }=(B↖{→})_{ \wire \AB }+(B↖{→})_{ \BC\Arc }

+(B↖{→})_{ \wire \CD }+(B↖{→})_{ \wire \PQ }

+(B↖{→})_{ \QR \Arc } +(B↖{→})_{ \wire \RS }

\B_\PQ=\B_\RS=0

B↖{→}_\BC=-B↖{→}_\QR

( B↖{→} )_{\wire \AB} = B↖{→}_ \CD

B↖{→} _\net= (B)_{\wire \AB} + (B)_{\wire \CD}

⇒{µ_0I}/{4πr}+{µ_0I}/{4πr}

B↖{→}_\net={µ_0I}/{2πr}

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