Question

Two circular coils P and Q are made from similar wires but the radius of Q is twice that of P. What should be the value of potential difference across them. So that the magnetic induction at their centres may be the same ?

• A. $V_q=2V_p$
  
• B. $V_q=3V_p$
  
• C. $V_q=4V_p$
  
• D. $V_q=\frac{1}{4}{V}_p$

Answer 1

The correct option is C $V_q=4V_p$


$B_p=\frac{{\mu }_0{I}_1}{2r_1}{B}_q=\frac{{\mu }_0{I}_2}{2r_2}{r}_2=2r_1{B}_p=B_q{I}_2=2I_1\frac{V_q}{V_p}=\frac{I_2\times r_2}{I_1\times r_1}=\frac{2I_1}{I_1}\times \frac{2r_1}{r_1}=\frac{4}{1}$