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AIIMS 2004
Exam
AIIMS
Year
2004
Subject
Physics
Chapter
Magnetic Effects of Current

AIIMS 2004 · Physics · Magnetic Effects of Current

A circular coil of radius R carries an electric current. The...

A circular coil of radius RR carries an electric current. The magnetic field due to the coil at a point on the axis of the coil located at a distance rr from the center of the coil, such that r>>Rr>>R, varies as

Options

  1. A1/r1 / r
  2. B1/r3/21 / r^{3 / 2}
  3. C1/r21 / r^2
  4. D1/r31 / r^3.

Correct answer

D. 1/r31 / r^3.

Step-by-step solution

Magnetic field at a point on the axis of a loop is given by B=μ04π2πIR2(R2+r2)3/2\frac{\mu_0}{4 \pi} \frac{2 \pi I R^2}{\left(R^2+r^2\right)^{3 / 2}}When r>>Rr \gt \gt R, B=μ04π2πR2Ir3=μ02πAIr3. Thus, \frac{\mu_0}{4 \pi} \frac{2 \pi R^2 I}{r^3}=\frac{\mu_0}{2 \pi} \frac{A I}{r^3} . \quad \text{ Thus, }B \propto\left(1 / r³\right) .
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