My teacher told that magnitude is the positive value of that quantity or the modulus of that quantity.
he also told that vector quantities have both magnitude and direction and scalar quantities have only magnitudes and hence are always positive.
However, gravitational potential energy is always negative except for being 0(at infinity)
But gravitational potential energy is also a scalar quantity.
So is there magnitude negative?
What I thought about it was that it's magnitude is negative.
Let's take an example of any vector quantity,say velocity.
If a body is moving with the velocity of -5m/s, that means it is moving with a speed of 5m/s in the direction opposite to the positive direction.
And here, the body is covering 5 meters every second, though it's velocity is -5m/s.
But if a body has potential energy -40J, it does not mean that it has actual potential energy 40J but is in opposite direction, hence the magnitude should be negative
Please tell me that will the magnitude be positive or negative?
Best Answer
Scalar quantities can be negative. Instead of saying "scalar quantities have only magnitudes," a better description might be that a scalar quantity can be described using only one number per point in space. That number may be positive or negative.
In contrast, a vector quantity cannot be described using only one number per point in space. In 3-d space, we need 3 numbers per point in space to describe a vector quantity.
The word "magnitude," whether applied to a scalar or a vector or anything else, normally refers to a non-negative number. It is sometimes used to refer to the absolute value of a scalar, and sometimes used to refer to the norm (e.g., length) of a vector.
In summary, this is how the words are typically used:
Scalar typically refers to a single element of a number field (or a single element per point in space), such as a real number (which can be positive or negative) or even a complex number (this is common in the context of quantum physics).
Magnitude typically refers to a non-negative real number.
The real culprit here is statements like "a vector has both magnitude and direction, but a scalar has only magnitude." The last part of that statement either (1) imposes an unconventional restriction on the usage of the word "scalar," or (2) exercises unconventional freedom in the usage of the word "magnitude."