Point charges in electric field

In summary, the metal sphere experiences a net force of zero due to the action of gravity and the electric field. The angle between the string and the vertical axis is 3.6 degrees.
  • #1
tuggler
45
0

Homework Statement



A metal sphere hangs from a string and has 6 kg of mass. The sphere has a charge of +3.7 µC. A uniform electric field is turned on and directed to the right.

(a). What is the electric force on the metal sphere if the magnitude of the electric field is
106 N/C?

(b). When the sphere reaches equilibrium, what is the angle that the string makes with the vertical axis (assuming the same electric field as part (a))?

18-p-034.gif


Homework Equations



[tex]F =ma[/tex] and [tex]F = Eq[/tex]

The Attempt at a Solution



I worked out (a) and got the force to be 3.7 N, but I don't know how to do part (b)?
 
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  • #2
When the sphere is in equilibrium, the sum of all the forces acting on must be zero. What are the forces?
 
  • #3
One of the force is the electric field moving the sphere to the right. But since you said the sum of all the forces acting on must be zero hence the sphere is in equilibrium doesn't it mean that there is no angle?
 
  • #4
tuggler said:
One of the force is the electric field moving the sphere to the right.

Any other forces?

But since you said the sum of all the forces acting on must be zero hence the sphere is in equilibrium doesn't it mean that there is no angle?

No, this does not follow. A balance scale, for example, may have many possible equilibrium positions, depending on the masses, and in all those positions the net force is zero.
 
  • #5
In (a), is that 106 N/C or 106 N/C?
 
  • #6
Gneill - Sorry, you're correct, it is 10^6 N/C.

Voko - Thanks for clearing that misconception. And to answer you question, there is also a gravitational force and an electric force.
 
  • #7
The electric force acts horizontally. The gravitational force acts vertically. The sum of just these two forces can never be zero.
 
  • #8
Hmm, I am still not understanding how to do the question.
 
  • #9
tuggler said:
Hmm, I am still not understanding how to do the question.

Draw the FBD for the sphere. You've calculated the magnitude of the electric force and you should know the direction in which it acts. You've stated that gravity is also acting. You know which direction that acts. So pencil them in. What's their net?

For the the sphere to be stationary the net force must be zero. So what additional force must balance the action of the others?
 
  • #10
I'm just going to add to what others have been saying.

First you will want to draw a free body diagram for your sphere. Being able to visualize the situation will simplify the problem. Remember to include all the forces acting on the sphere: there's the force of gravity, the force of the electric field and don't forget that the STRING will provide TENSION. So there are three forces you should include. Also, be sure to identify where the string is when at rest (just hanging) which will help you find on the FBD the angle you need to calculate (this isn't really necessary but it will help you visualize the situation).

That was the hardest part. Now, when in equilibrium, the net force on the sphere will be zero. This mean that [itex]\sum F_y=0[/itex] and [itex]\sum F_x=0[/itex]. Set both equation using data from your FBD. You will have two unknowns. Fortunately, we also have two equations! Finishing the problem should not be hard from here.
 
  • #11
You guys helped tremendously! Drawing a picture helped a lot. I got the degree to be 3.6 because the gravity pulling the sphere down was calculated to be F = ma = 6kg(9.8m/s^2) = 58. 8 N. I already calculated the electric force which exerts a force of 3.7 N to the right of the sphere. Then with these two forces I drew a picture and calculated the angle between them by using tan^-1(3.7/58.8) = 3.6 degrees.

Thanks again!
 

1. What is a point charge in an electric field?

A point charge is a hypothetical charge that has a very small size and is considered to be concentrated at a single point. It represents the fundamental building block of the electric field and can be either positive or negative.

2. How does a point charge interact with an electric field?

A point charge will experience a force when placed in an electric field. The direction of the force depends on the charge of the point charge and the direction of the electric field. A positive point charge will experience a force in the direction of the electric field, while a negative point charge will experience a force in the opposite direction.

3. What is the formula for calculating the electric field strength of a point charge?

The electric field strength at a point in space due to a point charge is given by the equation E = kQ/r^2, where k is the Coulomb's constant, Q is the magnitude of the point charge, and r is the distance from the point charge to the point where the electric field is being measured.

4. How does the distance from a point charge affect the electric field strength?

The electric field strength decreases as the distance from the point charge increases. This is because the electric field spreads out as it moves away from the point charge, leading to a weaker field at greater distances.

5. What is the difference between a point charge and a continuous charge distribution?

A point charge represents a single charge at a specific point in space, while a continuous charge distribution represents a collection of charges spread out over an area or volume. The electric field for a point charge is easier to calculate, while the electric field for a continuous charge distribution requires integration to find the total effect of all the charges.

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