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Class 12 › Physics › Moving Charges and Magnetism
CBSE2023Class Class 12 · Physics1 Marks · Long✅ Verified
Case Study (Charged particles): Particle 1 (charge $-q$) and particle 2 (charge $+2q$) enter the magnetic field $\vec{B}=B_0\hat{k}$ with velocities $\vec{v_1}=v_1\hat{i}$ and $\vec{v_2}=v_2\hat{i}$. Q: Then:
✅ Answer & Solution
Magnetic force: $\vec{F} = q\vec{v}\times\vec{B}$. For particle 1 ($q_1=-q$, $\vec{v_1}=v_1\hat{i}$): $\vec{v}\times\vec{B} = v_1\hat{i}\times B_0\hat{k} = v_1B_0(\hat{i}\times\hat{k}) = -v_1B_0\hat{j}$. With $q_1=-q$: $\vec{F_1} = (-q)(-v_1B_0\hat{j}) = +qv_1B_0\hat{j}$ (force along $+y$). For particle 2 ($q_2=+2q$, $\vec{v_2}=v_2\hat{i}$): $\vec{F_2} = (2q)(-v_2B_0\hat{j}) = -2qv_2B_0\hat{j}$ (force along $-y$). Since the initial forces are in opposite directions, the two particles curve in opposite senses. Working out the rotation sense: particle 1 turns anticlockwise while particle 2 turns clockwise. Hence the correct option is (D).