Two circular coils 1 and 2 are made from the | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let $r_{1}$ and $r_{2}$ be the radii of coil $1$ and $2$ respectively. Given $r_{1} = 2r_{2}$.The magnetic field at the center of a circular coil

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(C) Let $r_{1}$ and $r_{2}$ be the radii of coil $1$ and $2$ respectively. Given $r_{1} = 2r_{2}$.The magnetic field at the center of a circular coil is given by $B = \frac{\mu_{0} I}{2r}$.For the fields to be equal,$B_{1} = B_{2} \implies \frac{\mu_{0} I_{1}}{2r_{1}} = \frac{\mu_{0} I_{2}}{2r_{2}}$.Substituting $r_{1} = 2r_{2}$,we get $\frac{I_{1}}{2r_{2}} = \frac{I_{2}}{r_{2}}$,which simplifies to $I_{1} = 2I_{2}$.The resistance of a wire is proportional to its length,$R \propto L = 2\pi r$. Since both coils are made of the same wire,$R_{1} = 2R_{2}$.The potential difference is $V = IR$. Therefore,the ratio of potential differences is $\frac{V_{1}}{V_{2}} = \frac{I_{1} R_{1}}{I_{2} R_{2}}$.Substituting the values,$\frac{V_{1}}{V_{2}} = \frac{(2I_{2})(2R_{2})}{I_{2} R_{2}} = 4$.

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

Similar Questions

If the gravitational acceleration at the surface of the Earth is $g$,then the increase in potential energy in lifting an object of mass $m$ to a height equal to half of the radius of the Earth from the surface will be:

Which is the largest flower?

$A$ motor boat is travelling with a speed of $3.0 \, m/s$. If the force on it due to water flow is $500 \, N$,the power of the boat is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module