Two infinite length wires carry currents 8 A | vedclass

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

Question

(D) The magnetic field due to an infinitely long wire carrying current $I$ at a perpendicular distance $r$ is given by $B = \frac{\mu_0 I}{2 \pi r}$.F

Vedclass · Accepted Answer

$\frac{5 \mu_0}{\pi d}$

Vedclass · Answer

(D) The magnetic field due to an infinitely long wire carrying current $I$ at a perpendicular distance $r$ is given by $B = \frac{\mu_0 I}{2 \pi r}$.For the wire along the $X$-axis carrying current $I_1 = 6 \ A$,the magnetic field at $P(0, 0, d)$ is directed along the $Y$-axis (using the right-hand thumb rule). Thus,$\vec{B}_1 = \frac{\mu_0 I_1}{2 \pi d} \hat{j} = \frac{\mu_0 (6)}{2 \pi d} \hat{j} = \frac{3 \mu_0}{\pi d} \hat{j}$.For the wire along the $Y$-axis carrying current $I_2 = 8 \ A$,the magnetic field at $P(0, 0, d)$ is directed along the negative $X$-axis. Thus,$\vec{B}_2 = -\frac{\mu_0 I_2}{2 \pi d} \hat{i} = -\frac{\mu_0 (8)}{2 \pi d} \hat{i} = -\frac{4 \mu_0}{\pi d} \hat{i}$.The net magnetic field at $P$ is $\vec{B}_P = \vec{B}_1 + \vec{B}_2 = -\frac{4 \mu_0}{\pi d} \hat{i} + \frac{3 \mu_0}{\pi d} \hat{j}$.The magnitude of the magnetic field is $B_P = \sqrt{\left(-\frac{4 \mu_0}{\pi d}\right)^2 + \left(\frac{3 \mu_0}{\pi d}\right)^2} = \frac{\mu_0}{\pi d} \sqrt{16 + 9} = \frac{5 \mu_0}{\pi d}$.

Two infinite length wires carry currents $8 \ A$ and $6 \ A$ respectively and are placed along the $X$ and $Y$ axes respectively. The magnetic field at a point $P(0, 0, d)$ will be:

Similar Questions

Describe and illustrate the magnetic field lines produced by a current-carrying circular loop.

The magnetic field intensity at the centre of a circular wire of radius $0.1 \,m$ carrying a current of $0.2 \,A$ is:

$A$ 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?

$A$ current flows through a circular coil of radius $R$. Find the distance from the center on the axis where the magnetic field is $\frac{1}{8}$th of the magnetic field at the center.

Vedclass Test Series

Exam Paper Generator

Online Exam Module