The figure shows an arrangement of four charged particles, with angle θ = 37.0 ˚ and...

The figure shows an arrangement of four charged particles, with angle θ = 37.0 ˚ and distance d = 3.00 cm. Particle 2 has charge q₂ = 6.40 × 10^-19 C; particles 3 and 4 have charges q₃ = q₄ = -1.60 × 10^-19 C. (a) What is the distance D between the origin and particle 2 if the net electrostatic force on particle 1 due to the other particles is zero? (b) If particles 3 and 4 were moved closer to the x axis but maintained their symmetry about that axis, would the required value of D be greater than, less than, or the same as in part (a)?

this website has the figure

https://www.chegg.com/homework-help/questions-and-answers/figure-shows-arrangement-four-charged-particles-angle-theta-370-degree-distance-d-300-cm-p-q3603840?trackid=06f98d39478b&strackid=d121f996f8aa

Expert Solution

let dist of 3 and 4 from 1 be r then cos37 =d/r => r= d/cos37

Force due to 3 and 4 on 1 will have one horizontal component and one verticalcomponent each but the vertical components cancel out due to symmetry. and horizontal component will be cos 37 times the force=>

F3 = kq1q3/r^2 =kq1q3/d^2 *(cos37)^2 => horizontal component=F3cos37=kq1q3/d^2 *(cos37)^3 this is the same force by q4 also due to symmetry.

Force due to q2: kq1q2/(d+D)^2 since q2 have opposite sign from q3 , their forces will be opposite. so, for net force on q1 to be 0, F2= -2*F3cos37 =>kq1q2/(d+D)^2= - 2kq1q3/d^2 *(cos37)^3 =>-q2/2*q3=(cos37)^3 * (d+D)^2/d^2

cos37~0.8 , q₂ = 6.40 × 10^-19 C and q₃ = q₄ = -1.60 × 10^-19 C and d=0.03m=> 6.4/3.2 =0.512 (0.03+D)^2/0.0009

=> (0.03+D)^2 =2/568.89 => D= 0.059-0.03 = 0.029m

b)If particles 3 and 4 were moved closer to the x axis maintaining symmetry, the horizontal components due to these masses increase so, the opposing force due to q2 needs to increase so, 2 should be closer to 1 ie D will be lees than as of in part a

genius_generous answered 2 years ago

A figure shows four particles, each of mass 20.5 g, that form a square with an...

A figure shows four particles, each of mass 20.5 g, that form a square with an edge length of d = 0.480 m. If d is reduced to 0.160 m, what is the change in the gravitational potential energy of the four-particle system?

Given the two charged particles shown in the figure below, find the electric field at the...

Given the two charged particles shown in the figure below, find the electric field at the origin. (Let q1 = −26.00 nC and q2 = 7.00 nC. Express your answer in vector form.) q1 is at (2,4) and q2 is at (-2,3)

At a particular moment, three charged particles are located as shown in the figure below. Q1...

At a particular moment, three charged particles are located as shown in the figure below. Q1 = −4.5 μC, Q2 = +5.5 μC, and Q3 = −7.0 μC. Your answers to the following questions should be vectors. (Recall that 1 μC = 1 ✕ 10−6 C. Assume that the +x axis is to the right, the +y axis is up along the page and the +z axis points into the page. Express your answers in vector form.) (a) Find the...

Four equally charged particles with charge q are placed at the corners of a square with...

Four equally charged particles with charge q are placed at the corners of a square with side length L, as shown in the figure below. A fifth charged particle with charge Q is placed at the center of the square so that the entire system of charges is in static equilibrium. What are the magnitude and sign of the charge Q? (Use any variable or symbol stated above as necessary.) magnitude Q =

In the figure (Figure 1) a conducting rod of length L = 37.0 cm moves in...

In the figure (Figure 1) a conducting rod of length L = 37.0 cm moves in a magnetic field B⃗ of magnitude 0.500 T directed into the plane of the figure. The rod moves with speed v = 6.00 m/s in the direction shown. Part A What is the potential difference between the ends of the rod? Part C When the charges in the rod are in equilibrium, what is the magnitude of the electric field within the rod? Part...

What is the 2-component of vector E in terms of the angle θ and the magnitude E shown in (Figure 1)?

Part A What is the 2-component of vector E in terms of the angle θ and the magnitude E shown in (Figure 1)? Part B What is the y-component of vector E in terms of the angle θ and the magnitude E shown in (Figure 1)? Part C For the same vector, what is the z-component in terms of the angle ф and the magnitude

In the figure the four particles form a square of edge length a = 6.40 cm...

In the figure the four particles form a square of edge length a = 6.40 cm and have charges q1 = 8.91 nC, q2 = -19.0 nC, q3 = 19.0 nC, and q4 = -8.91 nC. What is the magnitude of the net electric field produced by the particles at the square's center?

The figure shows electrons 1 and 2 on an x axis and charged ions 3 and...

The figure shows electrons 1 and 2 on an x axis and charged ions 3 and 4 of identical charge -q and at identical angles θ. Electron 2 is free to move; the other three particles are fixed in place and are intended to hold electron 2 in place. For physically possible values of q ≤ 5e, what are the (a) smallest, (b) second smallest, and (c) third smallest values of θ for which electron 2 is held in place?

In the figure four particles form a square with edge lengtha = 4.68 × 10-2...

In the figure four particles form a square with edge length a = 4.68 × 10-2 m. The charges areq1 = q4 = 1.49 × 10-15 C and q2 = q3 = q. (a) What is q if the net electrostatic force on particle 1 is zero?(b) Is there any value of q that makes the net electrostatic force on each of the four particles zero?

In the figure four particles form a square with edge length a = 4.54 × 10-2...

In the figure four particles form a square with edge length a = 4.54 × 10-2 m. The charges are q1 = q4 = 2.20 × 10-15 C and q2 = q3 = q. (a) What is q if the net electrostatic force on particle 1 is zero? (b) Is there any value of q that makes the net electrostatic force on each of the four particles zero? Choose the answer for part (b) from the menu in accordance to...

Question