Two parallel long current-carrying wires sepa | vedclass

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

Question

(A) The magnetic field produced by a long straight wire at a distance $d$ is given by $B = \frac{\mu_0 I}{2 \pi d}$.For point $A$ (located at distance

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(A) The magnetic field produced by a long straight wire at a distance $d$ is given by $B = \frac{\mu_0 I}{2 \pi d}$.For point $A$ (located at distance $r$ from wire $1$ carrying current $I$ and distance $3r$ from wire $2$ carrying current $2I$):$B_A = \frac{\mu_0 I}{2 \pi r} + \frac{\mu_0 (2I)}{2 \pi (3r)} = \frac{\mu_0 I}{2 \pi r} + \frac{\mu_0 I}{3 \pi r} = \frac{3 \mu_0 I + 2 \mu_0 I}{6 \pi r} = \frac{5 \mu_0 I}{6 \pi r}$.For point $C$ (located at distance $3r$ from wire $1$ carrying current $I$ and distance $r$ from wire $2$ carrying current $2I$):$B_C = \frac{\mu_0 I}{2 \pi (3r)} + \frac{\mu_0 (2I)}{2 \pi r} = \frac{\mu_0 I}{6 \pi r} + \frac{2 \mu_0 I}{2 \pi r} = \frac{\mu_0 I + 6 \mu_0 I}{6 \pi r} = \frac{7 \mu_0 I}{6 \pi r}$.Taking the ratio:$\frac{B_A}{B_C} = \frac{5 \mu_0 I / 6 \pi r}{7 \mu_0 I / 6 \pi r} = \frac{5}{7}$.Given that the ratio is $\frac{x}{7}$,we find $x = 5$.

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 $\qquad$

Similar Questions

When a helium nucleus makes a full rotation of a circle of radius $0.8 \,m$ in $2.5 \,s$, then the value of magnetic field $B$ at the centre of the circle will be

$A$ circular loop of radius $0.0157\,m$ carries a current of $2.0\,A$. The magnetic field at the centre of the loop is $(\mu_0 = 4\pi \times 10^{-7}\,T\cdot m/A)$.

$A$ current of $1\,A$ is passed through a hexagonal conducting wire of side $1\,m$. The magnetic induction at its centre $O$ in $Wb/m^2$ will be

$A$ circular current-carrying coil has radius $R$. The magnetic induction at the centre of the coil is $B_{C}$. The magnetic induction of the coil at a distance $\sqrt{3} R$ from the centre along the axis is $B_{A}$. The ratio $B_{A}: B_{C}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module