The two parallel plates in FGURE CP27.31 are 2.0 cm apart and the eloctric field strength betwe

step 1 We have force equals mass times acceleration equals charge times electric field. So we have acce

The two parallel plates in FGURE CP27.31 are 2.0 cm apart...

The two parallel plates in FGURE CP27.31 are $2.0 \mathrm{~cm}$ apart and the eloctric field strength between them is $1.0 \times 10^4 \mathrm{~N} / \mathrm{C}$. An electron is launched at a $45^{\circ}$ angle from the positive plate. What is the maximom initial speed $v_0$ the electron can have without hitting the negative plate? plGuRe Cpat.71

Key Concepts

Uniform Electric Field

A uniform electric field is one in which the electric force on a charge is constant in both magnitude and direction at every point in the region. This concept is essential in understanding how charged particles, such as electrons, experience a constant acceleration when placed in such a field, much like the constant acceleration seen in gravitational fields in projectile motion.

Electric Force on a Charge

The electric force exerted on a charged particle in an electric field is given by the equation F = qE, where q is the charge of the particle and E is the electric field strength. This force is responsible for the acceleration of the particle and plays a similar role to gravitational force in classical kinematics, allowing us to apply similar methods to determine trajectories.

Projectile Motion in a Uniform Field

Projectile motion describes the two-dimensional movement of an object subject to a constant acceleration. When the acceleration is due not to gravity but to an electric force, the principles remain the same: the motion can be analyzed by decomposing it into horizontal and vertical components, where one component is unaffected by the electric field while the other is accelerated by it.

Decomposition of Motion

Decomposing the motion of a particle into perpendicular components simplifies analysis of its trajectory. In scenarios involving a constant force acting in one direction, such as an electric field, the motion in that direction can be calculated separately from the motion in the perpendicular direction. This is essential when determining conditions, such as maximum initial speeds, to avoid collision with boundaries.

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