Math Problem Statement
Solution
The problem consists of a setup involving two parallel plates separated by a distance of 20 cm, with a potential difference between them of -2V on the left plate and +10V on the right plate.
Let's break down the tasks in the question:
Part (a)
- Given: The potential difference varies linearly across the plates.
- Task: Find the equation for the potential as a function of distance , where corresponds to the -2V plate and meters (20 cm) corresponds to the +10V plate.
The general form for a linearly varying potential is: where is the slope and is the y-intercept.
Since the change in voltage is linear:
- The difference in potential between the plates is volts.
- The distance between the plates is meters.
The slope can be calculated as: Thus, the equation becomes:
Part (b)
- Given: A particle with mass and charge is located at the -2V plate initially.
- Task: Calculate the force acting on the particle, assuming it remains stationary, and then find its velocity after traveling a distance of 5 cm (0.05 m) from the -2V plate.
To solve part (b):
-
Electric Field (E): Since the potential varies linearly, the electric field is constant and given by:
-
Force (F): The force on a charge in an electric field is given by:
-
Acceleration (a): Using Newton's second law , we find the acceleration:
-
Velocity after traveling 5 cm: Assuming it starts from rest, we use :
Would you like a more detailed breakdown of any steps or further clarification?
Related Questions:
- How does the mass of the particle affect the final velocity?
- What would happen if the charge were positive instead of negative?
- How does the distance between the plates influence the electric field strength?
- If the particle had an initial velocity, how would that change the result?
- What is the effect of a non-linear potential distribution on the electric field?
Tip:
In problems involving a linearly varying electric potential, remember that the electric field will be constant and equal to the slope of the potential function.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Linear potential variation
Electric field calculation
Newton's second law
Kinematic equations
Formulas
V(x) = mx + c
E = -dV/dx
F = qE
a = F/m
v^2 = u^2 + 2as
Theorems
Linearly varying potential in an electric field
Newton's second law of motion
Suitable Grade Level
Undergraduate Physics
Related Recommendation
Calculate Potential and Particle Speed in a Uniform Electric Field Between Plates
Calculate Electric Field between Parallel Plates with Potentials 10V and -2V
Electric Field Between Parallel Plates with Potential Difference
Electric Field and Potential Difference in a Parallel Plate Capacitor Using Gauss's Law
Calculating the Potential Difference between Parallel Plates in an Electric Field