A loop,made of straight edges,has four corner | vedclass

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

Question

(D) The loop lies in the $xy$-plane with corners at $(L, L, 0)$,$(-L, L, 0)$,$(-L, -L, 0)$,and $(L, -L, 0)$.The side length of the square loop is $2L$

Vedclass · Accepted Answer

$4 B_0L^2 	ext{ Wb}$

Vedclass · Answer

(D) The loop lies in the $xy$-plane with corners at $(L, L, 0)$,$(-L, L, 0)$,$(-L, -L, 0)$,and $(L, -L, 0)$.The side length of the square loop is $2L$.Therefore,the area of the loop is $A = (2L) 	imes (2L) = 4L^2$.The area vector $\vec A$ is perpendicular to the $xy$-plane,so $\vec A = 4L^2 \hat k$.The magnetic field is given by $\vec B = B_0(\hat i + \hat k)$.The magnetic flux $\phi$ is given by the dot product of the magnetic field and the area vector:$\phi = \vec B \cdot \vec A$$\phi = B_0(\hat i + \hat k) \cdot (4L^2 \hat k)$$\phi = 4B_0L^2 (\hat i \cdot \hat k + \hat k \cdot \hat k)$Since $\hat i \cdot \hat k = 0$ and $\hat k \cdot \hat k = 1$,we get:$\phi = 4B_0L^2 (0 + 1) = 4B_0L^2 	ext{ Wb}$.

$A$ loop,made of straight edges,has four corners at $A(L, L, 0)$,$B(-L, L, 0)$,$C(-L, -L, 0)$,and $D(L, -L, 0)$. $A$ magnetic field $\vec B = B_0(\hat i + \hat k) \text{ T}$ is present in the region. The magnetic flux passing through the loop $ABCD$ is:

Similar Questions

What is the difference between Gauss's law in electrostatics and Gauss's law in magnetism?

Explain Gauss's law for magnetism.

$A$ square loop of side $2 \ m$ lies in the $Y-Z$ plane in a region having a magnetic field $\vec{B}=(5 \hat{i}+3 \hat{j}-4 \hat{k}) \ T$. The magnitude of magnetic flux through the square loop is (in $Wb$)

The radius of a coil of $N$ turns is $R$. If the plane of the coil is placed parallel to a uniform magnetic field $B$,then the flux linked with the coil is:

$A$ circular disc of radius $0.2 \; m$ is placed in a uniform magnetic field of induction $\frac{1}{\pi} \; Wb/m^2$ in such a way that its axis makes an angle of $60^{\circ}$ with $\vec{B}$. The magnetic flux linked with the disc is..... $Wb$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module