19 votes

Why do we associate negative sign to electric charges when they are a scalar quantity?

As a high school student, my knowledge of electrostatics is limited but what I am sure is that Signs are associated with quantities to show their direction (such quantities are called vector ...
Bob D's user avatar
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10 votes
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How many null directions are there?

The signature of the metric is determined by the eigenvalues of the metric. Using a convention where spacelike distances are positive and timelike distances are negative, the Minkowski metric (...
Andrew's user avatar
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8 votes
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In this conservation of momentum problem, where is the sign error coming from?

You have a choice of you keeping track of the vertical direction, or the math keeping track. Since you know one particle is going "up" and one particle is going "down", you can set ...
BowlOfRed's user avatar
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6 votes

Why do we associate negative sign to electric charges when they are a scalar quantity?

but what I am sure is that Signs are associated with quantities to show their direction (such quantities are called vector quantities) You shouldn't be too sure of this - unless you think of ...
Steeven's user avatar
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5 votes

In this conservation of momentum problem, where is the sign error coming from?

Let the upward y-direction be $\hat y$ $$0 = m_1 v_1 \sin(30) + m_2 v_2 \sin(60).\tag{2}$$ should be written as a vector equation $$0 \,\hat y = m_1 v_1 \sin(30)\,\hat y + m_2 v_2 \sin(60).\tag{2a} \,(...
Farcher's user avatar
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4 votes

Why do we associate negative sign to electric charges when they are a scalar quantity?

I think that you can blame Benjamin Franklin who had the idea that electricity was something to do with a fluid moving from one body to another. Excess fluid making some objects positive and a ...
Farcher's user avatar
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3 votes

Why do we associate negative sign to electric charges when they are a scalar quantity?

In physics, scalar, vectors and tensors in general, are defined with respect to transformations of space-time. For simplicity, let us use classical physics and say that the only symmetries of space ...
Mauricio's user avatar
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3 votes
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What is the locus of the velocity vectors of a boat navigating in the sea under the presence of some force?

We know from Newton's second law that $\displaystyle \vec F = \frac {d(m \vec v)}{dt}$ and as long as the mass $m$ of the boat is constant we can conclude that $\displaystyle \vec F = m \frac {d \vec ...
gandalf61's user avatar
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2 votes
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In equation of torque and angular momentum what is the position vector exactly

The $r$ in the equations for angular momentum or torque for example, is a position vector, however, the specifics of the vector depend on the problem you are working. For example, if you are wanting ...
Albertus Magnus's user avatar
2 votes

In this conservation of momentum problem, where is the sign error coming from?

The angle you have stated is 60° is really -60° or 300° and $-sin(60) = sin(300)$ Remember the right hand rule. With thumb up, the direction of increasing angle goes with the curl of your fingers.
Stevan V. Saban's user avatar
2 votes

Angular velocity relative to some frame

Consider the case where A is itself a rotating frame. In such case, the angular velocity with respect to frame A will be more than just the angular velocity of B in an inertial frame, it must also ...
Cort Ammon's user avatar
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2 votes

Why can't rotations in general be associated with vectors?

A vector can be a useful representation of a simple rotation about an axis. But rotations don't transform or "add" (compose) like vectors. Vector additions commute, but the result of ...
John Doty's user avatar
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1 vote

Vectors in inertial and non-inertial frames

This is a subtlety. You are correct that vectors are always independent of basis. The vector $\mathbf{A}$ is the same vector throughout and can be decomposed with respect to either the inertial or ...
Vincent Thacker's user avatar
1 vote
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Dot product in optics

When we use complex vectors, we work with bivectors. In general, the algebra of these bivectors is a natural and simple extension of the algebra of real vectors so that we do not insist on the ...
Vincent Fraticelli's user avatar
1 vote

Dot product in optics

Note that the scalar product on $\Bbb{C}^n$ must be hermitian instead of symmetric in order to ensure positive-definiteness. In consequence, one has indeed $\vec{E}_0 \cdot \vec{E}_0^* = \langle \vec{...
Abezhiko's user avatar
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1 vote

On covariant form of Lorentz equation

The first two expression are clearly not equivalent. The first is the low velocity limit of the second. The second equation is correct if $p^a$ denotes $mu^a = m \gamma dx^a/dt$ and $u^a = dx^a/dt$, ...
my2cts's user avatar
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1 vote
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Question regarding resultant of force vectors

Suppose the two forces are $\mathbf{F}_{1}$ and $\mathbf{F}_{2}$ so that the resultant is $\mathbf{F} = \mathbf{F}_{1} + \mathbf{F}_{2}$. Then we have that $\mathbf{F}_{2} = \mathbf{F} - \mathbf{F}_{1}...
kandb's user avatar
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1 vote

Why do we associate negative sign to electric charges when they are a scalar quantity?

Here are three ways of thinking about your dilemma. Charge is a scalar, and it is a real number: real numbers can be positive or negative. Charge is a measure of the number of electrons in an atom, ...
Simon Crase's user avatar
1 vote

Why do we associate negative sign to electric charges when they are a scalar quantity?

The simple answer to this question is that "It is just a convention". Sir Benjamin Franklin conducted many experiments (like the famous kite experiment), to explain the results of these ...
Amarnath Parasar's user avatar
1 vote

What is the locus of the velocity vectors of a boat navigating in the sea under the presence of some force?

Perhaps this result can help you ? for a 2D simple dynamic boat simulation where the velocity is constant and you have side wind disturbance , the y via x position of the boat look like this the ...
Eli's user avatar
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1 vote

What is the difference between a vector and a representation of a vector in QM?

The state vector $|\Psi\rangle$ "encodes" everything about a quantum state, because you can choose to expand $|\Psi\rangle$ in any orthonormal, complete basis corresponding to some ...
BioPhysicist's user avatar
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1 vote
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Understanding angular velocity $\omega$ as a vector

Your reasoning is correct. The angular velocity has to be normal to the plane of rotation. If it, or any component of it, lay in the plane of rotation, that vector quantity would have to be changing ...
Rich's user avatar
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1 vote

In equation of torque and angular momentum what is the position vector exactly

In mechanics, there are three places where this equation shows up, and it has the same geometric interpretation each time. In each case, the $\vec{r}$ is the vector from the origin (or the point of ...
John Alexiou's user avatar
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1 vote

Why is the force of gravity not equal to the normal force on an inclined plane?

Turn the question on its head. Ask yourself: Why would you expect the normal force to be equal to the gravitational force? There is no law stating this. There is no reason to thing that this should be ...
Steeven's user avatar
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