JEE Main · 2024 · 04 Apr 2024 · Shift 2 · Magnetic Effects of Current

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Two parallel long current carrying wire separated by a distance 2 r are shown in the figure. The ratio of magnetic field at A to the magnetic field produced at C is

\frac{X}{7}

. The value of x is ____.

Answer: 5

Solution

From the figure,

A

is at distance

r

from the wire carrying

I

and

3 r

from the wire carrying

2 I

;

C

is at distance

r

from the wire carrying

2 I

and

3 r

from the wire carrying

I

. Both currents flow the same way, so at each of these external points the two individual fields point in the same direction and add:

B_{A} = \frac{μ _{0} I}{2 π r} + \frac{μ _{0} ( 2 I )}{2 π ( 3 r )} = \frac{μ _{0} I}{2 π r} (1 + \frac{2}{3}) = \frac{5}{3} \cdot \frac{μ _{0} I}{2 π r}

B_{C} = \frac{μ _{0} ( 2 I )}{2 π r} + \frac{μ _{0} I}{2 π ( 3 r )} = \frac{μ _{0} I}{2 π r} (2 + \frac{1}{3}) = \frac{7}{3} \cdot \frac{μ _{0} I}{2 π r}

\frac{B _{A}}{B _{C}} = \frac{5}{7} ⟹ x = 5

JEE Main · 2024 · 04 Apr 2024 · Shift 2 · Integer answer

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JEE Main · 2024 · 04 Apr 2024 · Shift 2 · Magnetic Effects of Current

Solution

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