The electric current in a circular coil of fo | vedclass

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

Question

(C) The magnetic field at the centre of a circular coil with $N$ turns and radius $R$ is given by $B = \frac{\mu_0 N i}{2R}$.For the first coil,$N_1 =

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(C) The magnetic field at the centre of a circular coil with $N$ turns and radius $R$ is given by $B = \frac{\mu_0 N i}{2R}$.For the first coil,$N_1 = 4$ and $B_1 = 32 \ T$. So,$32 = \frac{\mu_0 \cdot 4 \cdot i}{2R_1} \implies 32 = \frac{2 \mu_0 i}{R_1}$.When the wire of length $L$ is unwound and rewound into a single turn $(N_2 = 1)$,the circumference remains the same: $L = 2\pi R_1 \cdot N_1 = 2\pi R_2 \cdot N_2$.Since $N_1 = 4$ and $N_2 = 1$,we have $4(2\pi R_1) = 1(2\pi R_2)$,which gives $R_2 = 4R_1$.The new magnetic field is $B_2 = \frac{\mu_0 N_2 i}{2R_2} = \frac{\mu_0 \cdot 1 \cdot i}{2(4R_1)} = \frac{\mu_0 i}{8R_1}$.Comparing $B_1$ and $B_2$: $\frac{B_2}{B_1} = \frac{\mu_0 i / 8R_1}{2 \mu_0 i / R_1} = \frac{1}{16}$.Therefore,$B_2 = \frac{B_1}{16} = \frac{32}{16} = 2 \ T$.

The electric current in a circular coil of four turns produces a magnetic induction $32 \ T$ at its centre. The coil is unwound and is rewound into a circular coil of a single turn. If the same current flows through the new coil,the magnetic induction at the centre will be $.......... \ T$.

Similar Questions

$A$ cylindrical conductor of radius $R$ carries a current $i$. The value of the magnetic field at a point, which is $R/4$ distance inside from the surface, is $10 \ T$. Find the value of the magnetic field at a point, which is $4R$ distance outside from the surface.

The magnetic field near a current-carrying conductor is given by

Surface charge density on a ring of radius $a$ and width $d$ is $\sigma$ as shown in the figure. It rotates with frequency $f$ about its own axis. Assume that the charge is only on the outer surface. The magnetic field induction at the centre is (Assume that $d \ll a$):

The ratio of the magnetic field at the centre of a current-carrying coil of radius $r$ to the magnetic field at a distance $r$ from the centre of the coil on its axis is $\sqrt{x}: 1$. The value of $x$ is $............$

Two parallel long current-carrying wires separated by a distance $2r$ are shown in the figure. The ratio of the magnetic field at $A$ to the magnetic field produced at $C$ is $\frac{x}{7}$. The value of $x$ is $\qquad$

Vedclass Test Series

Exam Paper Generator

Online Exam Module