# Charge on a particle to balance its weight

• Fluxthroughme
In summary, to find the charge of a 1.45g particle to remain stationary in a downward-directed electric field of magnitude 650N/C, we use the formula F = Eq = ma. Since the field points downwards, the charge must be negative to balance with gravity. Using the correct units, the charge is found to be -21.9 μC.
Fluxthroughme
1. What must the charge of a 1.45g particle be for it to remain stationary when placed in a downward-directed electric field of magnitude 650N/C?

## Homework Equations

$$E = \frac{F}{q}$$

## The Attempt at a Solution

So the field is pointing downwards. E fields point in the direction a positive charge would take, so the charge must be negative to stay balanced. Gravity is also pointing downwards.

So I take the above formula, and I get F = Eq = ma
$$q = \frac{(1.45*10^{-3})*g}{650} = 1.488*10^{-16} C$$
(Using g = $6.67*10^{-11}$) However the answer given is $-21.9\mu C$

Not sure what I'm doing wrong/missing here?

hey man welcome to physicsforums :)
Why are you using g=6.67*10^-11 ?

Edit: or, what units are these?

BruceW said:
hey man welcome to physicsforums :)
Why are you using g=6.67*10^-11 ?

I'm trying to balance the weight of the particle (mg) with the force from the electric field (Eq).

Thanks for the welcome ;D

Edit: the original particle is 1.45grams, so I use the $10^{-3}$ to convert that to kg. E is in N/C, and g, well I don't know :P Whatever the units of the gravitational constant are

Ohhhhh. I see what I've done! Doing dimensional analysis shows I have the wrong units; thanks for that.

I have to use 9.81 instead of the gravitational constant -_-

Thanks :P

Edit: Yeah, thanks ap123 :P I certainly won't make THAT mistake again ;D

g is the acceleration due to gravity, not the gravitational constant, ie g should be 9.80m/s2

Edit: OK - you've got it :)

## 1. How is the charge on a particle related to its weight?

The charge on a particle is related to its weight through the force of gravity. The greater the charge on a particle, the stronger the electric force between it and other charged particles. This force can counteract the force of gravity, resulting in a balanced weight.

## 2. What is the formula for calculating the charge on a particle to balance its weight?

The formula for calculating the charge on a particle to balance its weight is q = mg/E, where q is the charge, m is the mass of the particle, g is the acceleration due to gravity, and E is the electric field strength.

## 3. Can the charge on a particle be negative to balance its weight?

Yes, the charge on a particle can be negative to balance its weight. This means that the particle has an excess of electrons, which can create an attractive force with positively charged particles in the electric field, balancing out the weight of the particle.

## 4. How does the charge on a particle affect its motion in an electric field?

The charge on a particle affects its motion in an electric field by experiencing a force in the direction of the electric field. If the charge is positive, it will be attracted to the negative end of the electric field and vice versa for a negative charge. This force can cause the particle to move in a certain direction, depending on the strength and direction of the electric field.

## 5. Is the charge on a particle the only factor that affects its weight in an electric field?

No, the charge on a particle is not the only factor that affects its weight in an electric field. The mass of the particle and the strength of the electric field also play a role in determining the weight of the particle. A heavier particle will have a greater weight, even with the same charge, and a stronger electric field will result in a greater force on the particle, affecting its weight.

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