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NEET 2006
Exam
NEET
Year
2006
Subject
Physics
Chapter
Magnetic Effects of Current

NEET 2006 · Physics · Magnetic Effects of Current

Two circular coils 1 and 2 are made from the same wire but the...

Two circular coils 1 and 2 are made from the same wire but the radius of the 1st 1^{\text{st }} coil is twice that of the 2nd 2^{\text{nd }} coil. What potential difference in volts should be applied across them so that the magnetic field at their centres is the same?

Options

  1. A2
  2. B3
  3. C4
  4. D6

Correct answer

C. 4

Step-by-step solution

Let r1andr2r_1 and r_2 be the radius of coil 1 and coil 2 . If B1andB2B_1 and B_2 are magnetic induction at their centre then B1=μ0I12r1B_1=\frac{\mu_0 I_1}{2 r_1} and B2=μ0I22r2B1=B2andr1=2r2B_2=\frac{\mu_0 I_2}{2 r_2}B_1=B_2 and r_1=2 r_2 there I1=2I2I_1=2 I_2 Again if R1andR2R_1 and R_2 are resistance of the coil 2 then R1=2R2R_1=2 R_2 (as R∝R \propto length =2πr)=2 \pi r) and if v1andv2v_1 and v_2 are the potential difference across them respectively then V1V2=I1R1I2R2=(2I2)(2R2)I2R2=4\begin{aligned}\frac{V_1}{V_2}& =\frac{I_1 R_1}{I_2 R_2}\\ & =\frac{\left(2 I_2\right)\left(2 R_2\right)}{I_2 R_2}=4 \end{aligned}
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