An infinitely long wire lying along the Y-axi | vedclass

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

Question

(D) The magnetic field produced by an infinitely long straight wire carrying current $I$ at a distance $r$ from the wire is given by $B = \frac{\mu_0

Vedclass · Accepted Answer

Zero

Vedclass · Answer

(D) The magnetic field produced by an infinitely long straight wire carrying current $I$ at a distance $r$ from the wire is given by $B = \frac{\mu_0 I}{2 \pi r}$.In this problem,the wire lies along the $Y$-axis. The magnetic field lines are concentric circles in the $xz$-plane,centered on the $Y$-axis.The circular loop is in the $xy$-plane. The magnetic field vector $\vec{B}$ at any point on the loop lies in the $xz$-plane (specifically,it is perpendicular to the $Y$-axis and the radial vector from the wire).The area vector $\vec{A}$ of the loop in the $xy$-plane is directed along the $Z$-axis (i.e.,$\vec{A} = A \hat{k}$).Since the magnetic field $\vec{B}$ is always in the $xz$-plane and the area vector $\vec{A}$ is along the $Z$-axis,the magnetic field $\vec{B}$ is always perpendicular to the area vector $\vec{A}$ at every point on the loop.Therefore,the magnetic flux $\phi_B = \int \vec{B} \cdot d\vec{A} = \int B dA \cos(90^\circ) = 0$.

An infinitely long wire lying along the $Y$-axis carries a current $I$ as shown in the figure. What is the magnetic flux through a circular loop of radius $R$ in the $xy$-plane? [Assume $\mu_0$ is the magnetic permeability of free space.]

Similar Questions

The net magnetic flux through any closed surface is

Imagine rolling a sheet of paper into a cylinder and placing a bar magnet near its end as shown in the figure. What can you say about the sign of $\vec B \cdot d\vec A$ for every area element $d\vec A$ on the surface of the cylinder?

When does the magnetic flux become zero?

Which one of the following pairs of quantities and their units is a proper match?

$A$ square of side $x \, m$ lies in the $x-y$ plane in a region where the magnetic field is given by $\vec B = B_0 (3\hat i + 4\hat j + 5\hat k ) \, T$,where $B_0$ is a constant. The magnitude of the magnetic flux passing through the square is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module