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

(B) The magnetic field at the centre of a circular coil is given by $B = \frac{\mu_0 I}{2r}$.Given that the magnetic field at the centre is the same f

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(B) The magnetic field at the centre of a circular coil is given by $B = \frac{\mu_0 I}{2r}$.Given that the magnetic field at the centre is the same for both coils,we have:$\frac{\mu_0 I_1}{2(2r)} = \frac{\mu_0 I_2}{2(r)} \Rightarrow \frac{I_1}{I_2} = 2 \quad ...(i)$Since the coils are made from the same wire,their resistance $R$ is proportional to their length $l$ $(R = ho \frac{l}{A})$.The lengths are $l_1 = 2\pi(2r) = 4\pi r$ and $l_2 = 2\pi(r) = 2\pi r$.Thus,the ratio of resistances is $\frac{R_1}{R_2} = \frac{l_1}{l_2} = \frac{4\pi r}{2\pi r} = 2 \quad ...(ii)$Using Ohm's law,$V = IR$,we have $I = V/R$.Substituting this into equation $(i)$:$\frac{V_1/R_1}{V_2/R_2} = 2 \Rightarrow \frac{V_1}{V_2} = 2 	imes \frac{R_1}{R_2}$Substituting the ratio from equation $(ii)$:$\frac{V_1}{V_2} = 2 	imes 2 = 4$.

Two circular coils $1$ and $2$ are made from the same wire. The radius of the first coil is twice that of the second coil. What is the ratio of potential difference applied across them $V_1 / V_2$,so that the magnetic field at their centre is the same?

Similar Questions

Which of the following gives the value of the magnetic field according to Biot-Savart's law?

In the given figure,find the magnetic field at point $O$.

$A$ circular coil of wire consisting of $100$ turns,each of radius $8.0 \, cm$,carries a current of $0.40 \, A$. What is the magnitude of the magnetic field $B$ at the centre of the coil?

$A$ circular coil carrying current has radius $R$. The distance from the centre of the coil on the axis where the magnetic induction will be $\frac{1}{27}$th of its value at the centre of the coil is:

In a wire of radius $1 \ mm$,a steady current of $2 \ A$ uniformly distributed across the cross-section of the wire is flowing. Then the magnetic field at a point $0.25 \ mm$ from the centre of the wire is (in $\mu T$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module