Two particles X and Y having equal charges, after being...

Two particles $X$ and $Y$ having equal charges, after being accelerated through the same potential difference, enter a region of uniform magnetic field and describe circular paths of radii $R_{1}$ and $R_{2}$, respectively. The ratio of masses of $X$ and $Y$ is (A) $\left(\frac{R_{1}}{R_{2}}\right)^{1 / 2}$ (B) $\frac{R_{2}}{R_{1}}$ (C) $\left(\frac{R_{1}}{R_{2}}\right)^{2}$ (D) $\left(\frac{R_{1}}{R_{2}}\right)$

Two particles $X$ and $Y$ having equal charges, after being accelerated through the same potential difference, enter a region of uniform magnetic field and describe circular paths of radii $R_{1}$ and $R_{2}$, respectively. The ratio of masses of $X$ and $Y$ is
(A) $\left(\frac{R_{1}}{R_{2}}\right)^{1 / 2}$
(B) $\frac{R_{2}}{R_{1}}$
(C) $\left(\frac{R_{1}}{R_{2}}\right)^{2}$
(D) $\left(\frac{R_{1}}{R_{2}}\right)$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Acceleration through a Potential Difference

When a charged particle is accelerated by an electric potential difference, the work done on the particle converts into kinetic energy. This fundamental concept is captured by the relationship qV = ½mv², where q is the charge, V is the potential difference, m is the mass, and v is the velocity the particle attains after acceleration.

Circular Motion in a Magnetic Field

A charged particle moving in a uniform magnetic field experiences a Lorentz force, which is always perpendicular to its velocity. This force causes the particle to follow a circular path. The expression that relates the magnetic force to the centripetal force is qvB = mv²/r, where B is the magnetic field strength and r is the radius of the circular path.

Relationship Between Mass, Radius, and Velocity

By combining the equations for kinetic energy from acceleration (qV = ½mv²) and the magnetic force (qvB = mv²/r), one can derive how the radius of the circular path depends on the mass, velocity, and other parameters. This relationship, typically r ? m*v/(qB), is central when comparing different particles under the same accelerating conditions and magnetic field, allowing one to determine the ratio of their masses based on their circular path radii.

Transcript

Please give Ace some feedback