Concept explainers
A particle with electric charge q moves along a straight line in a uniform electric field
(b) Discuss the significance of the dependence of the acceleration on the speed. (c) What If? If the particle starts from rest it x = 0 at t = 0, how would you proceed to find the speed of the particle and its position at time t?
(a)
To show: The acceleration of the particle in the
Answer to Problem 39.88CP
Explanation of Solution
The formula to calculate the relative momentum is,
Here,
The formula to calculate the force on the electric charge is,
Here,
The formula to calculate the Force due to motion is,
The force on the electric charge due to motion must be equal to that of the force due to electric field.
Substitute
Substitute
Further solve the above equation.
The formula to calculate the acceleration is,
Substitute
Conclusion
Therefore, the acceleration of the particle in the
(b)
Answer to Problem 39.88CP
Explanation of Solution
The formula to calculate the acceleration of the charge is,
As the speed of charge approaches to the speed of light, the acceleration approaches to zero.
When the speed of the charge is very small as compared to that of the speed of the light the above equation can be transformed.
So the relative expression is transformed to the classical expression when the speed of the charge is very small as compared to that of the speed of the light.
Conclusion
Therefore, the significance of the dependence of the acceleration on the speed is that when the speed of the charge is very small as compared to that of the speed of light the relative expression is transformed to the classical expression.
(c)
Answer to Problem 39.88CP
Explanation of Solution
The formula to calculate the acceleration of the charge is,
Integrate the above equation from velocity
Thus the speed of the particle at time
The formula to calculate the position of the particle is,
Substitute
Integrate the above equation from position
Conclusion
Therefore, the speed of the charge particle at time
Want to see more full solutions like this?
Chapter 39 Solutions
Physics for Scientists and Engineers
- To study the properties of various particles, you can accelerate the particles with electric fields. A positron is a particle with the same mass as an electron but the opposite charge (+e). If a positron is accelerated by a constant electric field of magnitude 340 N/C, find the following. (a) Find the acceleration of the positron. m/s2(b) Find the positron's speed after 7.75 10-9 s. Assume that the positron started from rest. m/sarrow_forwardA charged particle moves under the influence of an electric field. Its x-position and y-position, as a function of time, are observed to be x(t) = 4 + 3t + t2 y(t) = 6− 4t + 0.5t2 meters, where the x- and y-direction are east and north, respectively. Letˆi andˆj denote unit vectors in the eastward and northward direction. a) At t = 2, what is the particle’s velocity? Express your answer as a vector usingˆi,ˆj notation, and also by specifying the magnitude and direction. b) At t = 2, what is the particle’s acceleration? Again, useˆi,ˆj notation,and also specify the magnitude and direction. c) How fast is the particle moving at the moment it is moving due east?arrow_forwardA proton initially moves left to right long the x axis at a speed of 9,070 m/s. It moves into an electric field, which points in the negative x direction, and travels a distance of 0.7 m before coming to rest. If the proton's mass and charge are 1.67 × 10−27 kg and 1.60 × 10−19 C respectively, what is the magnitude of the electric field?arrow_forward
- An electron is moving with an initial speed of 3.2 x 105 m/s toward a proton that is stationary. If the electron is very very far away from the proton initially, what distance from the proton does the electron have twice the speed it did originally? (Answer= 6.14x10^9)arrow_forwardA positively charged ball falls vertically along the lines of a uniform electric field. The weight of the ball is larger than the electric force. The air drag force, exerted on the ball, is directly proportional to its speed. The mass and charge of the ball are equal to 0.46 kg and 0.22 C. The magnitude of the electic field is 5 V/m. Determine the ratio v1/v2, where v1 and v2 are the speeds of steady (i.e., constant speed) motion when the electric field vector is oriented downwards and upwards, respectively.arrow_forwardA particle with electric charge q moves along a straight line in a uniform electric field E with speed u. The electric force exerted on the charge is qĒ. The velocity of the particle and the electric field are both in the x direc- tion. (a) Show that the acceleration of the particle in the x direction is given by du_ qE u3/2 a dt (b) Discuss the significance of the dependence of the accel- eration on the speed. (c) What If? If the particle starts from rest at x = 0 at i = 0, how would you proceed to find the speed of the particle and its position at time ?arrow_forward
- To study the properties of various particles, you can accelerate the particles with electric fields. A positron is a particle with the same mass as an electron but the opposite charge (+e). If a positron is accelerated by a constant electric field of magnitude 301 N/C, find the following. (a) Find the acceleration of the positron. (b) Find the positron's speed after 9.40 10-9 s. Assume that the positron started from rest.arrow_forward1) A proton (p) and electron (e-) are released when they are 4 Å (4 Angstroms). Find the initial accelerations of each particle, from one of the selections below. a) a(p) = 8.63 x 1017 m/s2, a(e-) = 1.58 x 1021 m/s2; b) a(p) = 3.4 x 1018 m/s2, a(e-) = 6.3 x 1021 m/s2; c) a(p) = 4.315 x 1016 m/s2, a(e-) = 7.9 x 1020 m/s2; d) a(p) = 3.45 x 1018 m/s2, a(e-) = 6.32 x 1021 m/s2. 1) Two small spheres are placed a distance 20 cm apart and have equal charge. How many excess electrons must be placed on each sphere if the magnitude of the Coulomb repulsive force is F = 3.33 x 10-21 N? a) 2 x 103; b) 350; c) 760; d) 1.2 x 103. 3)Three individual point charges are placed at the following positions in the x-y plane: Q3 = 5.0 nC at (x, y) = (0,0); Q2 = -3.0 nC at (x, y) = (4 cm, 0); and Q1 = ? nC at (x, y) = (2 cm,0); What is the magnitude, and sign, of charge Q1 such that the net force exerted on charge Q3, exerted by charges Q1 and Q2, is zero? a) Q1 = + 0.5 nC; b) Q1 = - 0.25 nC; c) Q1 = +…arrow_forwardThe drawing shows a proton with a speed v = 2.9 × 106 m/s moving toward a very long positively-charged plate with a charge density σ = 2.6 × 10-5 C/m2. What is the magnitude of the acceleration of the proton, in meters per squared second, as it approaches the charged plate?arrow_forward
- Newer automobiles have filters that remove fine particles from exhaust gases. This is done by charging the particles and separating them with a strong electric field. Consider a positively charged particle +3.1 µC that enters an electric field with strength 6 ✕ 106 N/C. The particle is traveling at 21 m/s and has a mass of 10−9 g. What is the acceleration of the particle? (Enter the magnitude only.)arrow_forwardA uranium ion and an iron ion are separated by a distance of, R=23.30 nm, as shown in the figure. The uranium atom is singly ionized; the iron atom is doubly ionized. Calculate the distance r from the uranium atom at which an electron will be in equilibrium. Ignore the gravitational attraction between the particles. What is the magnitude ?UFU of the force on the electron from the uranium ion?arrow_forwardA proton initially moves left to right along the x-axis at a speed of 7.0 × 103 m/s. It moves into an electric field, which points in the negative x-direction, and travels a distance of 0.70 m before coming to rest. What acceleration magnitude does the proton experience?arrow_forward
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning