Concept explainers
Figure 21-11 shows (1) four situations in which five charged particles are evenly spaced along an axis. The charge values are indicated except for the central particle, which has the same charge in all four situations. Rank the situations according to the magnitude of the net electrostatic force or the central particle, greatest first.
Figure 21-11 Question 1.
To rank:
The situations according to the magnitude of net electrostatic force exerted on the central particle by four given particles.
Answer to Problem 1Q
Solution:
Rank based on net electrostatic force is F3>F1>F2>F4
Explanation of Solution
1) Concept:
The net force acting on a particle due to more than one particle is the sum of forces exerted by each of the particles.
2) Formulae:
Electrostatic force between two charges q1 and q2,
k- Coulomb’s constant constant=8.99 x 109
d- distance of separation between particles.
3) Given:
a. The five particles are evenly spaced on an axis.
b. The charges on four particles are given except for the central particle.
Situation 1: Charges on right side = -e, -e Charges on left side =-+e, -e
Situation 2: Charges on right side = +e, +e Charges on left side =+e, -e
Situation 3: Charges on right side = -e, -e Charges on left side =+e, +e
Situation 4: Charges on right side = -e, +e Charges on left side =+e, -e
c. The central particle has same charge in all the 4 situations.
4) Calculation:
Let us consider that each of the particles is located at d distance apart.
Let us consider that the central particle has a charge +e.
According to Coulomb’s law, the magnitude of force F acting on the central particle due to the particles at distance d is,
Situation 1:
In the situation 1, the free body diagram of force acting on central particle, due to other particles is drawn as shown below.
|
|
|
|
|
The particles located at distance 2d on either side, exert equal and opposite forces on the central particle. So they nullify each other’s effect on the central particle. Meanwhile, the particles at distance d exert equal forces towards the same direction, and hence the exerted forces add up to 2F.
Hence net force, F1= 2F
Situation 2:
|
|
|
|
|
Force exerted by particles at distance d on either side nullifies each other. Hence, the net force on the central particle due to the particles at 2d distance,
F2 =
=
=
Situation 3:
|
|
|
|
|
Here the particles at distance ‘d’ exert equal force on same direction as in situation 1. Hence the force exerted by these particles on central particle is 2F. The particles that are at 2d distance on either sides again exert same force in same direction as in situation 2. Hence the force exerted by them on central particle is 0.5F.
Net force, F3= F1+F2 = 2F +0.5 F = 2.5 F
Situation 4:
|
|
|
|
|
Here the particles at distance ‘2d’ nullifies each other’s effect and also that are at distance ‘d’ again cancel the force exerted by each other. Therefore, the net force acting on the particle is zero.
Net force, F4=0
Conclusion:
We can find net electrostatic force acting on a particle by knowing the magnitude and direction of the forces exerted by each of the particles present in the system.
Want to see more full solutions like this?
Chapter 21 Solutions
Fundamentals Of Physics - Volume 1 Only
Additional Science Textbook Solutions
Biology: Life on Earth (11th Edition)
Campbell Biology (11th Edition)
Campbell Biology: Concepts & Connections (9th Edition)
Genetic Analysis: An Integrated Approach (3rd Edition)
Chemistry & Chemical Reactivity
Organic Chemistry (8th Edition)
- air is pushed steadily though a forced air pipe at a steady speed of 4.0 m/s. the pipe measures 56 cm by 22 cm. how fast will air move though a narrower portion of the pipe that is also rectangular and measures 32 cm by 22 cmarrow_forwardNo chatgpt pls will upvotearrow_forward13.87 ... Interplanetary Navigation. The most efficient way to send a spacecraft from the earth to another planet is by using a Hohmann transfer orbit (Fig. P13.87). If the orbits of the departure and destination planets are circular, the Hohmann transfer orbit is an elliptical orbit whose perihelion and aphelion are tangent to the orbits of the two planets. The rockets are fired briefly at the depar- ture planet to put the spacecraft into the transfer orbit; the spacecraft then coasts until it reaches the destination planet. The rockets are then fired again to put the spacecraft into the same orbit about the sun as the destination planet. (a) For a flight from earth to Mars, in what direction must the rockets be fired at the earth and at Mars: in the direction of motion, or opposite the direction of motion? What about for a flight from Mars to the earth? (b) How long does a one- way trip from the the earth to Mars take, between the firings of the rockets? (c) To reach Mars from the…arrow_forward
- No chatgpt pls will upvotearrow_forwarda cubic foot of argon at 20 degrees celsius is isentropically compressed from 1 atm to 425 KPa. What is the new temperature and density?arrow_forwardCalculate the variance of the calculated accelerations. The free fall height was 1753 mm. The measured release and catch times were: 222.22 800.00 61.11 641.67 0.00 588.89 11.11 588.89 8.33 588.89 11.11 588.89 5.56 586.11 2.78 583.33 Give in the answer window the calculated repeated experiment variance in m/s2.arrow_forward
- How can i solve this if n1 (refractive index of gas) and n2 (refractive index of plastic) is not known. And the brewsters angle isn't knownarrow_forward2. Consider the situation described in problem 1 where light emerges horizontally from ground level. Take k = 0.0020 m' and no = 1.0001 and find at which horizontal distance, x, the ray reaches a height of y = 1.5 m.arrow_forward2-3. Consider the situation of the reflection of a pulse at the interface of two string described in the previous problem. In addition to the net disturbances being equal at the junction, the slope of the net disturbances must also be equal at the junction at all times. Given that p1 = 4.0 g/m, H2 = 9.0 g/m and Aj = 0.50 cm find 2. A, (Answer: -0.10 cm) and 3. Ay. (Answer: 0.40 cm)please I need to show all work step by step problems 2 and 3arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning