JEE Main 2022 · Physics · Magnetic Effects of Current · medium

Two long straight insulated wires lie in the same plane, along the x-axis and the y-axis, crossing at the origin without electrical contact. The wire…

Numerical answer

Two long straight insulated wires lie in the same plane, along the

x

-axis and the

y

-axis, crossing at the origin without electrical contact. The wire along the

x

-axis carries

6\ \mathrm{A}

in the

+x

direction and the wire along the

y

-axis carries

8\ \mathrm{A}

in the

+y

direction. The magnitude of the net magnetic field at the point

(10\ \mathrm{cm},\,10\ \mathrm{cm})

\mu\mathrm{T}

is (

\mu_0=4\pi\times10^{-7}\ \mathrm{T\,m\,A^{-1}}

)

Show answer and solution

Answer: 4

Each wire is at perpendicular distance

0.1\ \mathrm{m}

from the point, with

B=\dfrac{\mu_0I}{2\pi d}=2\times10^{-7}\dfrac{I}{0.1}

B_x=1.2\times10^{-5}\ \mathrm{T}

(from

6\ \mathrm{A}

) and

B_y=1.6\times10^{-5}\ \mathrm{T}

(from

8\ \mathrm{A}

). By the right-hand rule, the

x

-wire gives

\hat x\times\hat y=+\hat z

at the point (above it), while the

y

-wire gives

\hat y\times\hat x=-\hat z

(the point lies to its right). The fields are opposite, so

B_{net}=16-12=4\ \mu\mathrm{T}

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