Question

The ratio of the magnetic fields produced at the centre of a solenoid for a flow of current $1A$ to that produced inside toroid for the flow of current $2A$ both having same number of turns per unit length is

• A. $1:1$
• B. $1:2$
• C. $2:1$
• D. $1:4$
• E. $4:1$

Answer 1

The correct option is B $1:2$

Given, $i_{sol}=1A$ and $i_{tor}=2A$
Magnetic field in solenoid is
$B_S={\mu }_{0}n{i}_{sol}....\left(i\right)$
Magnetic field in toroid is
$B_t={\mu }_{0}n{i}_{br}....\left(ii\right)$
On dividing Eq. (i) by Eq. (ii), we get
$\frac{B_s}{B_t}=\frac{{\mu }_{0}n{i}_{sol}}{{\mu }_{0}n{i}_{tor}}\Rightarrow \frac{B_s}{B_t}=\frac{i_{sol}}{i_{tor}}=\frac{1}{2}$.