Two parallel wires situated at a distance 2a | vedclass

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

Question

(A) The magnetic field due to a long straight wire at a distance $r$ is given by $B = \frac{\mu_0 i}{2\pi r}$.Since the currents are in opposite direc

Vedclass · Accepted Answer

$\frac{\mu_0 ia}{\pi r^2}$

Vedclass · Answer

(A) The magnetic field due to a long straight wire at a distance $r$ is given by $B = \frac{\mu_0 i}{2\pi r}$.Since the currents are in opposite directions,the magnetic field vectors $B_1$ and $B_2$ at point $P$ will have the same magnitude $B = \frac{\mu_0 i}{2\pi r}$.From the geometry of the figure,the vertical components of the magnetic fields cancel each other,while the horizontal components add up.The angle between the horizontal axis and the magnetic field vector is $	heta$,where $\sin 	heta = \frac{a}{r}$.The resultant magnetic field $B_{net} = B_1 \cos 	heta + B_2 \cos 	heta = 2B \cos 	heta$.Since $\cos 	heta = \sqrt{1 - \sin^2 	heta} = \sqrt{1 - (a/r)^2} = \frac{\sqrt{r^2 - a^2}}{r}$.However,looking at the geometry,the horizontal component is $B \sin 	heta$ (based on the angle $	heta$ shown with the vertical). Let's re-evaluate: The angle $	heta$ is between the vertical and the field vector. The horizontal component is $B \sin 	heta$.$B_{net} = 2B \sin 	heta = 2 \left( \frac{\mu_0 i}{2\pi r} ight) \left( \frac{a}{r} ight) = \frac{\mu_0 ia}{\pi r^2}$.

Two parallel wires situated at a distance $2a$ are carrying equal currents $i$ in opposite directions as shown in the figure. The value of the magnetic field at a point $P$ situated at equal distances $r$ from both the wires will be:

Similar Questions

$A$ 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

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

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

Two circular coils are made from the same wire,but the radius of the $1^{\text{st}}$ coil is twice that of the $2^{\text{nd}}$ coil. If the magnetic field at their centers is the same,then the ratio of the potential difference applied across them is ($1^{\text{st}}$ to $2^{\text{nd}}$ coil).

Vedclass Test Series

Exam Paper Generator

Online Exam Module