A uniform,constant magnetic field vec B is di | vedclass

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

Question

(A) The magnetic moment $\vec m$ of the square loop is given by $\vec m = I_0 A \hat n,$ where $A = L^2$ is the area and $\hat n$ is the unit vector n

Vedclass · Accepted Answer

$\vec 	au = \frac{B I_0 L^2}{\sqrt 2} (- \hat i + \hat j)$

Vedclass · Answer

(A) The magnetic moment $\vec m$ of the square loop is given by $\vec m = I_0 A \hat n,$ where $A = L^2$ is the area and $\hat n$ is the unit vector normal to the loop. Since the loop is in the $xy-$ plane,$\hat n = \hat k.$ Thus,$\vec m = I_0 L^2 \hat k.$The magnetic field $\vec B$ is in the $xy-$ plane at an angle of $45^o$ to the $x-$ axis,so $\vec B = B \cos 45^o \hat i + B \sin 45^o \hat j = \frac{B}{\sqrt 2} (\hat i + \hat j).$The torque $\vec 	au$ is given by $\vec 	au = \vec m 	imes \vec B.$$\vec 	au = (I_0 L^2 \hat k) 	imes \left( \frac{B}{\sqrt 2} (\hat i + \hat j) ight)$$\vec 	au = \frac{I_0 L^2 B}{\sqrt 2} (\hat k 	imes \hat i + \hat k 	imes \hat j)$Using the cross product rules $\hat k 	imes \hat i = \hat j$ and $\hat k 	imes \hat j = -\hat i,$$\vec 	au = \frac{I_0 L^2 B}{\sqrt 2} (\hat j - \hat i) = \frac{B I_0 L^2}{\sqrt 2} (- \hat i + \hat j).$

Similar Questions

$A$ circular coil carrying a current of $2.5 \ A$ is free to rotate about an axis in its plane perpendicular to an external magnetic field. When the coil is made to oscillate, the time period of oscillation is $T$. If the current through the coil is $10 \ A$, the time period of oscillation is:

$A$ $250$-turn rectangular coil of length $2.1\, cm$ and width $1.25\, cm$ carries a current of $85\, \mu A$ and is subjected to a magnetic field of strength $0.85\, T.$ The work done to rotate the coil by $180^o$ against the torque is .............. $\mu J$.

$A$ uniform magnetic field of $0.3 \text{ T}$ is established along the $+z$-direction. $A$ rectangular loop of sides $10 \text{ cm}$ and $5 \text{ cm}$ carries a current of $12 \text{ A}$ and is placed in the $xy$-plane as shown in the figure. The torque acting on the loop is $....... \text{ Nm}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module