Class 12 NEET Physics Moving Charges and Magnetism

Concept: To keep a charged particle moving horizontally, gravity must be balanced. Electric force can balance gravity, and magnetic force can also balance gravity — but each requires specific field orientations.Explanation:The particle has weight $mg$ acting downward.$$mg = 10^{-2} \times 10 = 0.1 \text{ N}$$To keep the particle moving horizontally, the net vertical force must be zero.Analyzing each statement:Statement (1): $\vec{B}$ ⊥ velocity, $\vec{E}$ along velocity.

• $\vec{E}$ along velocity → Electric force along velocity (horizontal) → cannot balance gravity (vertical). ❌

Statement (2): Both $\vec{B}$ and $\vec{E}$ along velocity direction.

• $\vec{E}$ along velocity → Electric force horizontal only → cannot balance gravity.
• $\vec{B}$ along velocity → Magnetic force $= qvB\sin(0°) = 0$ → no magnetic force.
• Neither can balance gravity alone here... BUT if $\vec{E}$ is along velocity (horizontal), it provides no vertical force. Wait — actually if $\vec{B}$ is along velocity, magnetic force is zero. So this seems wrong too.

Let me re-examine: Statement (2) — $\vec{B}$ along velocity means $F_{mag} = q\vec{v} \times \vec{B} = 0$. $\vec{E}$ along velocity means $F_E$ is horizontal. Neither balances gravity. ❌ ...Actually, re-reading: the question asks which pair is POSSIBLE, meaning each statement individually can keep the particle horizontal.Statement (3): $\vec{B}$ and $\vec{E}$ mutually perpendicular and both perpendicular to velocity.

• Let velocity be along $\hat{x}$, $\vec{E}$ along $\hat{y}$ (vertical, upward) → $F_E = qE$ upward, can balance $mg$. ✓
• $\vec{B}$ along $\hat{z}$ → $F_{mag} = qvB$ along $\hat{y}$ (vertical) → can also balance $mg$. ✓
• This is possible. ✓

Statement (4): $\vec{B}$ along velocity, $\vec{E}$ perpendicular to velocity.

• $\vec{B}$ along velocity → $F_{mag} = 0$
• $\vec{E}$ perpendicular to velocity (e.g., vertical/upward) → $F_E = qE$ upward → can balance $mg$ ✓
• This is possible. ✓

Verification of Statement (1): $\vec{E}$ along velocity → $F_E$ horizontal, cannot balance gravity. ❌So the possible statements are (3) and (4).Answer: B. (3) and (4)