Finding the Electric Field Needed to Suspend a Charged Bead

AI Thread Summary
To determine the electric field needed to suspend a charged bead, the problem involves balancing the electrostatic force with the gravitational force acting on the bead. The bead's mass and charge are given, allowing the calculation of the gravitational force using F = mg. The electrostatic force is expressed as F = Eq, where E is the electric field strength and q is the charge. By equating the gravitational force to the electrostatic force, the electric field can be calculated as E = mg/q. The final calculation suggests an electric field strength of approximately 4.9 x 10^-11 N/C is required to suspend the bead.
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1. Homework Statement
A 5.0×10^−2g plastic bead is charged by the addition of 1.0×10^10 excess electrons. What electric field (strength) will cause the bead to hang suspended in the air?


2. Homework Equations



3. The Attempt at a Solution
It has something to do with F = Eq but i don't know where to go about there
 
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Welcome to PF.

Let's see.

You figure F = E*q.

And if you draw a force diagram, what does E*q need to balance with?

They give you the mass ... hmm, what could you do with that?
 
So..

F=Eq

E=F/q - we know q but we need F.

For it to hang suspended, there needs to be no net force acting on the bead. The electrostatic force is one of two forces acting on the bead; as well as being the F in our equation. So...this "other force" needs to be equal to the electrostatic force.

Find the magnitude of this other force acting on the bead (the mass of the bead will come in handy...hint hint). As said, this force will be equal to the electrostatic force. Plug that into the above equation and solve for E. Good luck!
 
i'm assuming F= ma which leads to F = Mg but how does work into the equation

so mg = E*q

E = 4.9e-11 ?
 
Last edited:
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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