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JIPMER 2017
Exam
JIPMER
Year
2017
Subject
Physics
Chapter
Magnetic Effects of Current

JIPMER 2017 · Physics · Magnetic Effects of Current

In the given figure, what is the magnetic field induction at point...

In the given figure, what is the magnetic field induction at point OO. In the given figure, what is the magnetic field induction at point O .

Options

  1. Aμ0l4πr\frac{\mu_0 l}{4 \pi r}
  2. Bμ0l4r+μ0l2πr\frac{\mu_0 l}{4 r}+\frac{\mu_0 l}{2 \pi r}
  3. Cμ0I4r+μ0I4πr\frac{\mu_0 I}{4 r}+\frac{\mu_0 I}{4 \pi r}
  4. Dμ0I4r−μ0I4πr\frac{\mu_0 I}{4 r}-\frac{\mu_0 I}{4 \pi r}

Correct answer

C. μ0I4r+μ0I4πr\frac{\mu_0 I}{4 r}+\frac{\mu_0 I}{4 \pi r}

Step-by-step solution

Magnetic field due to straight wire above OO is zero i.e. B1=0B_1=0 (since, θ=0∘\theta=0^{\circ} ) The magnetic field due to semi circular part B2=(μ0nI2r)=μ0(1/2)I2r=μ0I4rB_2=\left(\frac{\mu_0 n I}{2 r}\right)=\frac{\mu_0(1 / 2) I}{2 r}=\frac{\mu_0 I}{4 r} The magnetic field due to lower straight portion B3=12μ0I2πr (upward) NetmagneticfieldB_3=\frac{1}{2} \frac{\mu_0 I}{2 \pi r} \text{ (upward) } Net magnetic fieldB=B_1+B_2+B_3 =0+μ0I4r+μ0I4πr\frac{\mu_0 I}{4 r}+\frac{\mu_0 I}{4 \pi r} (upwards) \text{ (upwards) }
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