Question

after being accelerated, the particle enters a uniform magnetic field of strength b0 and travels in a circle of radius r (determined by observing where it hits on a screen--as shown in the figure). the results of this experiment allow one to find m/q in terms of the experimentally measured quantities such as the particle radius, the magnetic field, and the applied voltage. what is m/q ?

Answer 1

The mass-to-charge ratio (m/q) can be determined experimentally by measuring the radius (r) of the particle's circular path, the magnetic field strength (B), and the velocity (v).

Step-by-step explanation:

The ratio of the mass to charge (m/q) of a particle can be determined by measuring the radius of the particle's circular path in a uniform magnetic field. When a charged particle with mass m and charge q enters a uniform magnetic field of strength B, it moves in a circular path of radius r. The equation for the radius of curvature (r) is given by:

r = (mv)/(qB)

By rearranging the equation, we can solve for m/q:

m/q = (Br)/(v)

Therefore, the mass-to-charge ratio (m/q) can be determined experimentally by measuring the radius (r) of the particle's circular path, the magnetic field strength (B), and the velocity (v).

Answer 2

To find the mass-to-charge ratio (m/q) of a particle in a magnetic field, we equate the magnetic force to the centripetal force needed for circular motion. By rearranging the equation, m/q can be expressed as v/rB, where v is the speed determined from the applied voltage, and r is the measured radius of the particle's circular path.

Step-by-step explanation:

To determine the ratio of the mass to the charge of a particle (m/q) that is moving in a circular path in a magnetic field, we use the principles of charged particles in magnetic fields. According to the Lorentz force, a charged particle that moves in a magnetic field experiences a force perpendicular to its velocity and magnetic field, which results in a circular motion for a velocity perpendicular to the field. The particle's centripetal force, needed to maintain the circular motion, is provided solely by the magnetic force.

From the Lorentz force equation and assuming that the velocity is perpendicular to the field (as stated), we have:

Force (magnetic) = qvB

Where q is the charge, v is the speed of the particle, and B is the magnetic field strength.

The centripetal force required for circular motion is given by:

Force (centripetal) = mv²/r

Equating the magnetic force to the centripetal force, we get:

qvB = mv²/r

By rearranging the equation, we can solve for m/q:

m/q = v/rB

where r is the observed radius of the particle's path and v is the speed, which can be determined from the kinetic energy provided by the applied voltage, thus allowing for the determination of m/q in terms of experimentally measured quantities.