If the electric field strength is increased to about 3.0 ×10^6 N / C air "breaks down" and loses

step 1 Question number 62 for part a, we know that the acceleration is given as force upon mass and for

If the electric field strength is increased to about 3.0...

If the electric field strength is increased to about $3.0 \times 10^{6} \mathrm{N} / \mathrm{C}$ air "breaks down" and loses its insulating quality. Under these conditions, sparking results. a. What acceleration does an electron experience when the electron is placed in such an electric field? b. If the electron starts from rest when it is placed in an electric field under these conditions, in what distance does it acquire a speed equal to 10,0 percent of the speed of light? c. What acceleration does a proton experience when the proton is placed in such an electric field?

If the electric field strength is increased to about $3.0 \times 10^{6} \mathrm{N} / \mathrm{C}$ air "breaks down" and loses its insulating quality. Under these conditions, sparking results.
a. What acceleration does an electron experience when the electron is placed in such an electric field?
b. If the electron starts from rest when it is placed in an electric field under these conditions, in what distance does it acquire a speed equal to 10,0 percent of the speed of light?
c. What acceleration does a proton experience when the proton is placed in such an electric field?

Key Concepts

Particle Properties

The intrinsic properties of particles, such as their mass and charge, critically influence how they respond to an electric field. Electrons, which have a relatively small mass and a negative elementary charge, will experience much higher accelerations compared to protons, which have a much larger mass but the same magnitude of electric charge (albeit positive). Understanding these differences is crucial when comparing the behaviors of different particles under similar electric field conditions.

Acceleration of a Charged Particle

When a charged particle is subjected to an electric field, the force acting on it causes acceleration, as described by Newton's second law, a = F/m. Consequently, a particle's acceleration in an electric field can be calculated using the formula a = qE/m. This equation shows that the acceleration depends not only on the strength of the electric field and the magnitude of the charge but also inversely on the mass of the particle.

Uniformly Accelerated Motion

Uniformly accelerated motion deals with objects whose acceleration remains constant over time. In such cases, kinematic equations can be used to relate the velocity, acceleration, and distance traveled. One of the fundamental equations is v² = 2ad, which can be rearranged to solve for the distance over which a particle reaches a particular speed. This principle is often applied in scenarios where charged particles accelerate in an electric field starting from rest.

Electric Field

The electric field is a vector field around a charged particle or object in which a force would be experienced by a test charge. It characterizes how the electric force is distributed in space and is measured in newtons per coulomb (N/C). When the strength of the electric field reaches a critical value, like the breakdown field of air, the medium can no longer effectively insulate, leading to phenomena such as sparking or electrical discharge.

Force on a Charged Particle

A charged particle placed within an electric field experiences a force that is directly proportional to both the charge of the particle and the strength of the electric field. This relationship is given by the equation F = qE, where F is the force, q is the charge of the particle, and E is the electric field strength. This concept is fundamental in understanding how charged particles are accelerated or deflected by electric fields.

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