CBSE 2025, Set 3

Question

**Assertion (A):** A charged particle is moving with velocity $v$ in $x	ext{-}y$ plane, making an angle $	heta$ ($0 < 	heta < \frac{\pi}{2}$) with x-axis. If a uniform magnetic field $\vec{B}$ is applied in the region, along y-axis, the particle will move in a helical path with its axis parallel to x-axis.

**Reason (R):** The direction of the magnetic force acting on a charged particle moving in a magnetic field is along the velocity of the particle. A). Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A). B). Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A). C). Assertion (A) is true, but Reason (R) is false. D). Both Assertion (A) and Reason (R) are false.

Edvaya · Accepted Answer

The correct answer is Both Assertion (A) and Reason (R) are false.. **Step 1: Check Assertion (A)**
The velocity $\vec{v}$ has components in the x and y directions ($v_x \hat{i} + v_y \hat{j}$). The magnetic field is along the y-axis ($\vec{B} = B \hat{j}$).
The component $v_y$ is parallel to $\vec{B}$ and will cause the particle to move linearly along the y-axis. The component $v_x$ is perpendicular to $\vec{B}$ and will cause circular motion in the x-z plane.
The resultant path is a helix, but its central axis will be parallel to the magnetic field direction, which is the **y-axis**, not the x-axis. (Assertion is **False**).

**Step 2: Check Reason (R)**
The magnetic force is given by Lorentz force law $\vec{F} = q(\vec{v} 	imes \vec{B})$. This force is always **perpendicular** to both the velocity $\vec{v}$ and the magnetic field $\vec{B}$, not along the velocity. (Reason is **False**).

Thus, both A and R are false.

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Physics > Magnetism Induction And Alternating Current > Moving Charges And Magnetism

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