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JEE Main 20246 AprilMorning Shift
Exam
JEE Main
Year
2024
Date
6 April
Shift
Morning Shift
Subject
Physics
Chapter
Magnetic Effects of Current

JEE Main 2024 · 6 April · Morning Shift · Physics · Magnetic Effects of Current

An element Δ l=Δ x i is placed at the origin and carries a large...

An element Δl=Δxi^\Delta l=\Delta x \hat{i} is placed at the origin and carries a large current I=10 AI=10 \mathrm{~A}. The magnetic field on the yy-axis at a distance of 0.5 m0.5 \mathrm{~m} from the elements Δx\Delta x of 1 cm1 \mathrm{~cm} length is: An element Δ l=Δ x i is placed at the origin and carries a large current I=10 ~A . The magnetic field on the y -axis at

Options

  1. A4×10−8 T4 \times 10^{-8} \mathrm{~T}
  2. B10×10−8 T10 \times 10^{-8} \mathrm{~T}
  3. C8×10−8 T8 \times 10^{-8} \mathrm{~T}
  4. D12×10−8 T12 \times 10^{-8} \mathrm{~T}

Correct answer

A. 4×10−8 T4 \times 10^{-8} \mathrm{~T}

Step-by-step solution

dB→=μ0I4π(dl→×r→)r3( Tesla) =10−7×10×(12×1100)(+k^)(12)3=4×10−8T(+k^)\begin{aligned} \overrightarrow{\mathrm{dB}} & =\frac{\mu_0 \mathrm{I}}{4 \pi} \frac{(\overrightarrow{\mathrm{d} l} \times \overrightarrow{\mathrm{r}})}{\mathrm{r}^3}(\text{ Tesla) } \\ & =\frac{10^{-7} \times 10 \times\left(\frac{1}{2} \times \frac{1}{100}\right)(+\hat{\mathrm{k}})}{\left(\frac{1}{2}\right)^3}=4 \times 10^{-8} \mathrm{ T}(+\hat{\mathrm{k}})\end{aligned}
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