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--- courses:phy102:7 [2023/03/13 08:26] – created - external edit 127.0.0.1
+++ courses:phy102:7 [2023/03/13 20:06] (current) – [5. Force and torque on a current loop] asad
@@ Line 56: / Line 56: @@
 Apply $\vec{F} = I\vec{l}\times \vec{B}$ on 4 sides.
+$$ \vec{F}_1 = IaB \sin(90^\circ-\theta)\hat{i} = IaB\cos\theta\hat{i} $$
+$$ \vec{F}_3 = - IaB \sin(90^\circ+\theta)\hat{i} = - IaB\cos\theta\hat{i} $$
+$$ \vec{F}_2 = IbB \hat{k} $$
+$$ \vec{F}_4 = - IbB \hat{k} $$
+$$ \sum \vec{F} = \vec{F}_1 + \vec{F}_2 + \vec{F}_3 + \vec{F}_4 = 0 $$
+But the net torque is not zero.
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+$$ \sum \vec{\tau} = \vec{\tau}_2 + \vec{\tau}_4 = F_2x\sin\theta\hat{i} - F_4(a-x)\sin\theta\hat{i} = -IabB\sin\theta\hat{i} = - IAB\sin\theta\hat{i} $$
+Define magnetic dipole moment as $\vec{\mu} = NIA\hat{n} $ and write
+$$ \vec{\tau} = \vec{\mu} \times \vec{B}. $$
+And potential energy for a magnetic dipole $U=-\vec{\mu} \cdot \vec{B}$.
 ===== - Hall effect =====