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  • Solve! - As shown in the figure , two infinitely long , identical wires are bent by 90oand placed in such a - Magnetic Effects of Current and Magnetism - JEE Main

As shown in the figure , two infinitely long , identical wires are bent by 90o and placed in such a way that the segments LP and QM are along the x-axis ,while segments PS and QN are parallel to the y-axis. . If OP = OQ = 4 cm , and the magnitude of the magnetic field at O is 10-4 T , and the two wires carry equal currents (see figure) , the magnitude of the current in each wire and the direction of the magnetic field at O will be 

(\mu_{0} = 4\pi x 10-7 NA-2) :

  • Option 1)

    20 A , perpendicular out of the page

  • Option 2)

    40 A ,  perpendicular out of the page

  • Option 3)

    20 A,  perpendicular into the page

  • Option 4)

    40 A,  perpendicular into the page

Answers (1)

best_answer

 

Magnetic Field Due to a Straight Wire -

B=\frac{\mu_{o}i}{4\pi r}(\sin\phi_{1}+\sin\phi_{2})

- wherein

Magnetic field at O

B_{O}=B_{PS}+B_{QN}+B_{LP}+B_{MQ}

B_{O}=B_{PS}+B_{QN}+O+O

Direction of   B_{PS} &  B_{QN} is both inward

Let current is i

Then  B_{PS}=B_{QN}=\frac{u_{0}i}{4\pi r}

 

B_{0}=2\times \frac{u_{0}i}{4\pi r}=\frac{u_{0}i}{2\pi r}

10^{-4}=\frac{u_{0}\times i}{2\pi r}=\frac{2\times 10^{-7}\times i}{4\times 10^{-2}}

i=20A


Option 1)

20 A , perpendicular out of the page

Option 2)

40 A ,  perpendicular out of the page

Option 3)

20 A,  perpendicular into the page

Option 4)

40 A,  perpendicular into the page

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