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NEET 2012
Exam
NEET
Year
2012
Subject
Physics
Chapter
Magnetic Effects of Current

NEET 2012 · Physics · Magnetic Effects of Current

Two similar coils of radius R are lying concentrically with their...

Two similar coils of radius RR are lying concentrically with their planes at right angles to each other. The currents flowing in them are II and 2I2 I, respectively. The resultant magnetic field induction at the centre will be

Options

  1. A5μ0I2R\frac{\sqrt{5} \mu_0 I}{2 R}
  2. B3μ0I2R\frac{3 \mu_0 I}{2 R}
  3. Cμ0I2R\frac{\mu_0 I}{2 R}
  4. Dμ0IR\frac{\mu_0 I}{R}

Correct answer

A. 5μ0I2R\frac{\sqrt{5} \mu_0 I}{2 R}

Step-by-step solution

The magnetic field (B)(B) at the centre of circular current carrying coil of radius RR and current I,B=μ0I2RI, B=\frac{\mu_0 I}{2 R} Similarly, if current =2I=2 I, then Magnetic field =μ02I2R=2B\text{Magnetic field }=\frac{\mu_0 2 I}{2 R}=2 B So, resultant magnetic field =B2+(2B)2=5B2=5B=μ0I52R\begin{aligned} & =\sqrt{B^2+(2 B)^2}=\sqrt{5 B^2}=\sqrt{5 B} \\ & =\frac{\mu_0 I \sqrt{5}}{2 R} \end{aligned}
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