A current carrying loop placed in a uniform magnetic field as shown in the figure. The magnitude of torque on the loop is (α π I r2 B/8). Find α.

Question

A current carrying loop placed in a uniform magnetic field as shown in the figure. The magnitude of torque on the loop is (α π I r2 B/8). Find α. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

vecτ= vecM × vecB, where vecM=(π r2 I) hati and vecB=B( hatk) ⇒ vecτ=(π I r2 B)( hati × hatk)=(π I r2 B)(- hatj)

Q. A current carrying loop placed in a uniform magnetic field as shown in the figure. The magnitude of torque on the loop is $\frac{α π I r ^{2} B}{8}$ . Find $α$ .

$τ = M \times B$ , where $M = (π r^{2} I) \hat{i}$ and $B = B (\hat{k})$
$\Rightarrow τ = (π I r^{2} B) (\hat{i} \times \hat{k}) = (π I r^{2} B) (- \hat{j})$

Q. A current carrying loop placed in a uniform magnetic field as shown in the figure. The magnitude of torque on the loop is 8απIr2B​. Find α.

τ=M×B, where M=(πr2I)i^ and B=B(k^) ⇒τ=(πIr2B)(i^×k^)=(πIr2B)(−j^​)

Q. A current carrying loop placed in a uniform magnetic field as shown in the figure. The magnitude of torque on the loop is $\frac{α π I r ^{2} B}{8}$ . Find $α$ .

$τ = M \times B$ , where $M = (π r^{2} I) \hat{i}$ and $B = B (\hat{k})$
$\Rightarrow τ = (π I r^{2} B) (\hat{i} \times \hat{k}) = (π I r^{2} B) (- \hat{j})$