Two infinitely long straight wires lie in the xy - plane along the...

Two infinitely long straight wires lie in the xy - plane along the lines

x = \pm R

. The wire located at

x = + R

carries a constant current

I_{1}

and the wire located at

x = - R

carries a constant current

I_{2}

. A circular loop of radius R is suspended with its centre at

(0, 0 \sqrt{3} R)

and in a plane parallel to the xy - plane. This loop carries a constant current

I

in the clockwise direction as seen from above the loop. The current in the wire is taken to be positive if it is in the

+ \hat{j}

direction. Which of the following statements regarding the magnetic field

\vec{B}

is (are) true?

I_{1} = I_{2}, t h e n \vec{B}

cannot be equal to zero at the origin

(0, 0, 0)

I_{1} > 0 a n d I_{2} < 0, t h e n \vec{B}

can be equal to zero at the origin

(0, 0, 0)

I_{1} < 0 a n d I_{2} > 0, t h e n \vec{B}

can be equal to zero at the origin

(0, 0, 0)

I_{1} = I_{2}

, Then the z-component of the magnetic field at the centre of the loop is \((-\mu 0 \mathrm{I} / 2 \mathrm{R})\)

Solution:

(A)

At origin,

\vec{B} = 0

due to two wires if

I_{1} = I_{2}, h e n c e ({\vec{B}}_{n e t})

at origin is equal to

\vec{B}

due to ring, which is non-zero.

(B)

I_{1} > 0 a n d I_{2} < 0, \vec{B}

at origin due to wires will be along

+ \hat{k}

direction and

\vec{B}

due to ring is along

- \hat{k}

direction and hence

\vec{B}

can be zero at origin

(C)

I_{1} < 0 a n d I_{2} > 0, \vec{B}

at origin due to wires is along

- \hat{k}

and also along

- \hat{k}

due to ring, hence

\vec{B}

cannot be zero

(D)

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Two infinitely long straight wires lie in the xy - plane along the...

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Find Colleges

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IIT Madras

IIT Delhi

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IIT Kanpur

IIT Kharagpur

IIT Roorkee

IIT Guwahati

IIT Hyderabad

IIT BHU

IIT Dhanbad

IIT Indore

IIT Gandhinagar

IIT Ropar

IIT Jodhpur

IIT Mandi

IIT Patna

Top Exams

Two infinitely long straight wires lie in the xy - plane along the...

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