Physics

Problem

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? [Adv. 2018] a. If

I_1 = I_2

, then

\vec{B}

cannot be equal to zero at the origin

(0, 0, 0)

b. If

I_1 > 0

and

I_2 < 0

, then

\vec{B}

can be equal to zero at the origin

(0, 0, 0)

c. If

I_1 < 0

and

I_2 > 0

, then

\vec{B}

can be equal to zero at the origin

(0, 0, 0)

d. If

I_1 = I_2

, then the

z

-component of the magnetic field at the centre of the loop is

\left(-\frac{\mu_0 I}{2R}\right)