In each of six situations, a particle (mass m, charge q ) is...

In each of six situations, a particle (mass $m$, charge $q$ ) is located at a point where the electric field has magnitude $E .$ No other forces act on the particles. Rank them in order of the magnitude of the particle's acceleration, from largest to smallest. (a) $m=6$ pg, $q=5 \mathrm{nC}, E=40 \mathrm{N} / \mathrm{C}$ (b) $m=3$ pg, $q=-5$ nC, $E=40 \mathrm{N} / \mathrm{C}$ (c) $m=3$ pg, $q=-10 \mathrm{nC}, E=80 \mathrm{N} / \mathrm{C}$ (d) $m=6$ pg, $q=-1$ nC, $E=200 \mathrm{N} / \mathrm{C}$ (e) $m=1$ pg $, q=3 \mathrm{nC}, E=300 \mathrm{N} / \mathrm{C}$ (f) $m=3$ pg, $q=-1$ nC, $E=100 \mathrm{N} / \mathrm{C}$

In each of six situations, a particle (mass $m$, charge $q$ ) is located at a point where the electric field has magnitude $E .$ No other forces act on the particles. Rank them in order of the magnitude of the particle's acceleration, from largest to smallest.
(a) $m=6$ pg, $q=5 \mathrm{nC}, E=40 \mathrm{N} / \mathrm{C}$
(b) $m=3$ pg, $q=-5$ nC, $E=40 \mathrm{N} / \mathrm{C}$
(c) $m=3$ pg, $q=-10 \mathrm{nC}, E=80 \mathrm{N} / \mathrm{C}$
(d) $m=6$ pg, $q=-1$ nC, $E=200 \mathrm{N} / \mathrm{C}$
(e) $m=1$ pg $, q=3 \mathrm{nC}, E=300 \mathrm{N} / \mathrm{C}$
(f) $m=3$ pg, $q=-1$ nC, $E=100 \mathrm{N} / \mathrm{C}$

Key Concepts

Comparative Analysis Using Proportional Relationships

When ranking different situations by acceleration, one can compare the ratios of qE to m. This approach ignores the sign of the charge when considering magnitude, emphasizing that a larger qE/m ratio results in a higher acceleration. This proportional reasoning is key when comparing different cases with varying masses, charges, and field strengths.

Acceleration of a Charged Particle in an Electric Field

By combining the electric force equation with Newton's Second Law, the acceleration produced on a charged particle by an electric field can be expressed as a = (qE)/m. This formula highlights that the acceleration is directly proportional to the charge and the electric field strength, and inversely proportional to the mass of the particle.

Electric Force on a Charged Particle

In an electric field, a charged particle experiences an electric force given by the equation F = qE, where q is the charge of the particle and E is the electric field strength. This relationship shows that the force is directly proportional to the magnitude of both the charge and the field.

Newton's Second Law

Newton's Second Law establishes that the net force acting on an object is equal to the product of its mass and its acceleration (F = ma). This fundamental principle connects dynamics with forces, allowing us to determine how a force results in acceleration when the mass is known.

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