Two Particles Are Fixed On An X Axis

[Violette Ransone]

Figure22-26 shows two charged particles fixed in place on an axis. (a) Where on the axis (other than at an infinite distance) is there a point at which their net electric field is zero: between the charges, to their left, or to their right? (b) Is there a point of zero net electric field anywhere offthe axis (other than at an infinite distance)?

Now, considering the point at the left of both the charges will contradict the above calculation case as field line from positive charge will be radially outward from the charge towards the point that implies the net field will subtract each other.

(a) In Checkpoint 4, if the dipole rotates from orientation 1 to orientation 2, is the work done on the dipole by the field positive, negative, or zero? (b) If, instead, the dipole rotates from orientation 1 to orientation 4, is the work done by the field more than, less than, or the same as in (a)?

I have managed to control the number of particles and to randomize the size, but I cannot randomize their orientation on their z axis. I have tried every control I can and none of them will allow me to do that.

SOLUTION: Hair works for me, but emitter shows nothing, so I need to use hair. Global Z is the right setting. But then I need to select the particle (not the emitter) and tab into edit mode and select the entire object and rotate it until it appears upright on the emitter. Then, while still in edit mode, I need to move it until the origin point is at the bottom of the object. The result is that the object ends up lying on its side, but the particles are standing upright on the emitter - very strange, but developers move in mysterious ways and I never complain about Blender developers. Then to rotate it on the Z axis, I need to use the Random Phase slider as suggested by a59303.

Learning a bit more about how particle systems work can help. Understanding how particle are born during emission, they have a lifetime, and that they die can make it easier to get them do what you want.

Two positively charged particles shown in figure are fixed in place on an x axis. The charges are q1 =1.60x10-19 C and q2 =3.20x10-19 C, and the particle separation is R=0.02 m. What are the magnitude and direction of the electrostatic force F12 on particle 1 from particle 2?

Since the two charges are both positively charged they will repel each other, therefore, the direction of the electrostatic force is repulsive (in other words, the electrostatic force is directed away from particle 2).

A rigid body is an idealization of a body that does not deform or change shape. Formally it is defined as a collection of particles with the property that the distance between particles remains unchanged during the course of motions of the body. Like the approximation of a rigid body as a particle, this is never strictly true. All bodies deform as they move. However, the approximation remains acceptable as long as the deformations are negligible relative to the overall motion of the body.

As an example, the flutter of an aircraft wing during the course of a flight is clearly negligible relative to the motion of the aircraft as a whole. On the other hand, if one was interested in stresses induced in the wing as a consequence of the flutter, these deformations become of primary importance.

In the following we will derive expressions that describe the general motion of a rigid body in the plane. As rigid bodies are viewed as collections of particles, this may appear an insurmountable task, requiring a description of the motion of each particle. However, the assumption that the body does not deform is a very strong one, requiring that the distance between every pair of particles comprising the body remains unchanged. To satisfy this, the particles that comprise a rigid body must move in concert, making the kinematics almost trivial.

In the course so far particle motion has been described using position vectors that were referred to fixed reference frames. The positions, velocities and accelerations determined in this way are referred to as absolute. Often it isn’t possible or convenient to use a fixed set of axes for the observation of motion. Many problems are simplified considerably by the use of a moving reference frame.

In the following, we identify two properties of the motion of rigid bodies that simplify the kinematics significantly. In order to do this, observe that an arbitrary rigid body motion falls into one of the three categories:

We proceed by demonstrating that every motion of a planar rigid body is associated with a single angular velocity and angular acceleration , describing the angular displacement of an arbitrary line inscribed in the body relative to a fixed direction.

Consider a rigid body undergoing plane motion. The angular positions of two arbitrary lines 1 and 2 attached to the body are specified by and measured relative to any convenient fixed reference direction. These are related to the intermediate angle shown as,

Observe that as the body is rigid, requiring that the distance between each pair of points on the two lines 1 and 2 is constant, angle must be invariant. Differentiating the relation above with this in mind,

Next, consider the motion of a rigid body over the interval as shown, with arbitrary point taken as reference. Clearly, the motion can be consider to occur in two stages: a translation with reference taking arbitrary line to an intermediate position ; and a rotation about point taking to its final position . This corresponds to a decomposition of the motion into the sum of a translation and a rotation. While the translational motion is described by the velocity and acceleration of the reference point, the rotational motion is characterized by the unique angular velocity and angular acceleration associated with the body. Thus, we have the property that the motion of a rigid body can be decomposed into a translation of an arbitrary point within the body, followed by a rigid rotation of the body about this point. Further, the motion of an arbitrary point within the body is determined completely once the translational quantities and , and rotational quantities and are known.

Now, as the body moves, point A traces a circular path of radius relative to point B, keeping the distance between the two unchanged. The angular velocity of this motion is simply the angular velocity of the rigid body. Then, using results derived previously for the time derivatives of rotating vectors we have:

Observe that the expression reflects the decomposition of rigid body motion referred to previously. With B chosen as reference, the velocity of A is the vector sum of a translational portion and a rotational portion .

In the following we will apply the kinematical relations derived to the case of a rigid body rotating about a fixed axis. As will be seen, the relations will reduce to familiar forms once n-t coordinates are introduced.

Consider an arbitrary point A of a rigid body rotating with angular velocity and angular acceleration about axis O. Let and be unit vectors tethered to point A as shown, with tangent and normal to the path of A. Then, using the kinematical relations for general rigid motion with axis O taken as reference, we obtain expressions for the velocity and acceleration of point A:

or the velocity of a point in the body is perpendicular to the line connecting the point to the axis of rotation, with magnitude proportional to its distance from the axis. The acceleration, on the other hand, is composed of the two pieces:

When working with n-t coordinates, care must be taken to ensure that a consistence choice of tangent vectors is made as two conventions exist for rotational quantities in the plane. The two differ in the first taking counter-clockwise rotations to be positive, which is recommended,

Therefore, in order to describe the motion of A, all that is necessary is a determination of for all time during the motion. Now, as angular velocity and angular acceleration describe the rotation of any line in the body, we have the relations

We proceed now to develop techniques to analyze the motion of rigid bodies in contact. We consider two contacting rigid bodies, and assume that no sliding occurs at the contacting surfaces. Let A and B be points, one on each of the rigid bodies, instantaneously in contact. As contact takes place without slipping, the velocity of A relative to B must vanish, or

An example of this form of contact is that between gears in a gear train: spur, bevel, helical or worm gears. In our consideration of planar motion, however, we are limited to analyzing contact between gears that have a common axis of rotation.

With the case of planar fixed axis rotation dealt with, we turn now to the more complex situation of general plane motion. Recall, once again, that the motion of an arbitrary rigid body can be reduced to the superposition of a translation and a fixed axis rotation. Handling the translation of a rigid body is trivial, all points of the body move with the same velocity and acceleration, and we now know how to deal with fixed axis rotations. Therefore, all that remains is to understand how the two are superposed. As we will find out, this is quite simple.

We proceed by returning to the equations we had derived for the arbitrary motion of a rigid body. Recall that these related the velocity and acceleration of a point A in the body to the translational motion of an arbitrary reference point B ( and ), and the absolute rotational motion of the body ( and ) as,

I am trying to calculate the Radial Distribution function of some particles. In the outcome plot x-axis is in pixels although I have given the units (Analyze-> Set Scale). Do I miss something?

Is there something else I should Do?

Thanks all!!!

Particles orient to face forward towards the camera position. Similar to the Face Camera Plane mode, however, here particles face towards the camera itself, appearing identical even at the edge of the screen.

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