Some electrostatics questions

In summary, electrostatics is a branch of physics that studies the behavior of electrically charged particles at rest. An electric field is a region of space around a charged particle or object in which a force is exerted on other charged particles. Electric charge is measured in units of coulombs (C) using an instrument called an electroscope. Conductors are materials that allow electricity to flow through them easily, while insulators are materials that do not allow electricity to flow through them easily. Coulomb's law states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
  • #1
musicfairy
101
0
Can someone please check my answers and explain if I get any wrong?

04e38.jpg


1. A point charge +Q is inside an uncharged conducting spherical shell that in turn is near several isolated point charges, as shown above. The electric field at point P inside the shell depends on the magnitude of
(A) Q only
(B) the charge distribution on the sphere only
(C) Q and the charge distribution on the sphere
(D) all of the point charges
(E) all of the point charges and the charge distribution on the sphere

Is it E? Electric field doesn't only depend on what's in the enclosed surface, does it?

04e4546.jpg


Particles of charge Q and -4Q are located on the x-axis as shown in the figure above. Assume the particles are isolated from all other charges.

2. Which of the following describes the direction of the electric field at point P?
(A) + x
(B) + y
(C) - y
(D) Components in both the - x and + y directions
(E) Components in both the + x and - y directions

E, it's attracted to -4Q, so it's direction would be toward -4Q, or -y and +x

3. At which of the labeled points on the x-axis is the electric field zero? (same picture as above)

(A) A
(B) B
(C) C
(D) D
(E) E



I should put it closer to the charge with a lesser magnitude so I'm guessing B?


04e57.jpg


4. What is the magnitude of the resultant electric field at the center of the circle?

Without even looking all the answers, I'll have to say that E = 0. Is this correct?


5. A uniform spherical charge distribution has radius R. Which of the following is true of the electric field strength due to this charge distribution at a distance r from the center of the charge?
(A) It is greatest when r = 0.
(B) It is greatest when r = R/2.
(C) It is directly proportional to r when r > R.
(D) It is directly proportional to r when r < R.
(E) It is directly proportional to r2.

Is it C?

04e69.jpg


When a negatively charged rod is brought near, but does not touch, the initially uncharged electroscope shown above, the leaves spring apart (I). When the electroscope is then touched with a finger, the leaves collapse (II). When next the finger and finally the rod are removed, the leaves spring apart a second time (III). The charge on the leaves is
(A) positive in both I and III
(B) negative in both I and III
(C) positive in I, negative in III
(D) negative in I, positive in III
(E) impossible to determine in either I or III



Is it A?



Please help.
 
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  • #2
musicfairy said:
Is it E? Electric field doesn't only depend on what's in the enclosed surface, does it?
Doesn't it? What does Gauss's law say?

When you put some charges around (or inside) a conducting sphere, what happens to the charge carriers (electrons) on the surface of the sphere?

musicfairy said:
E, it's attracted to -4Q, so it's direction would be toward -4Q, or -y and +x
Yes, but it is also repelled by the Q charge, which will contribute something with positive x AND positive y components to the electric field. So I'd say you have to argue a bit more precise.

musicfairy said:
3. At which of the labeled points on the x-axis is the electric field zero? (same picture as above)
I should put it closer to the charge with a lesser magnitude so I'm guessing B?
When in doubt, calculate.
I suppose you know the expression for the electric field, and by symmetry it is easy to see that the y-component is zero anyway. So you just need to consider the x-component for points on the x-axis; suppose the one charge is at x = 1 and the other at x = -1... what is the x-component of the total E-field as a function of x?

musicfairy said:
4. What is the magnitude of the resultant electric field at the center of the circle?

Without even looking all the answers, I'll have to say that E = 0. Is this correct?
Why?

musicfairy said:
5. A uniform spherical charge distribution has radius R. Which of the following is true of the electric field strength due to this charge distribution at a distance r from the center of the charge?
You should be able to find this in any electromagnetism textbook... what do you know about the electric field outside a uniform spherical charge distribution? (Actually, IIRC it goes for any spherical charge distribution). What do you know about the field (or potential) inside it?

musicfairy said:
When a negatively charged rod is brought near, but does not touch, the initially uncharged electroscope shown above, the leaves spring apart (I). When the electroscope is then touched with a finger, the leaves collapse (II). When next the finger and finally the rod are removed, the leaves spring apart a second time (III). The charge on the leaves is ...
So it must be A or B, because the leaves spring apart so the charges are equal on both. The question is then to determine whether the charge is positive or negative... you say it is positive. Can you explain why?
 
  • #3


Hello! I am happy to assist with your electrostatics questions. Let's go through each one and make sure you have a clear understanding of the concepts involved.

1. The correct answer is (C) Q and the charge distribution on the sphere. This is because the electric field at point P is influenced by both the point charge +Q inside the shell and the charge distribution on the conducting spherical shell. The electric field inside the shell is affected by the charge distribution on the surface of the shell.

2. The correct answer is (E) Components in both the +x and -y directions. This is because the electric field at point P is influenced by both the point charge Q and the point charge -4Q, which have opposite charges and therefore create electric fields in opposite directions.

3. The correct answer is (B) B. This is because at point B, the electric field from the point charge Q is equal in magnitude but opposite in direction to the electric field from the point charge -4Q, resulting in a net electric field of zero.

4. The correct answer is not E=0. The magnitude of the resultant electric field at the center of the circle can be calculated using the superposition principle, which states that the total electric field at a point is the vector sum of the individual electric fields from all the charges present. In this case, the electric field at the center of the circle will be non-zero since there are multiple charges present.

5. The correct answer is (E) It is directly proportional to r2. This is because the electric field strength due to a uniform spherical charge distribution is inversely proportional to the square of the distance from the center of the charge. This relationship is known as the inverse square law.

For the last question, the correct answer is (C) positive in I, negative in III. This is because in (I), the negatively charged rod induces a positive charge on the leaves of the electroscope, causing them to repel. When the electroscope is touched with a finger in (II), the negative charge is transferred to the ground, leaving the leaves with a positive charge. When both the finger and the rod are removed in (III), the leaves will again repel due to the positive charge present.

I hope this helps clarify any confusion you may have had. Keep up the good work with your electrostatics questions!
 

1. What is electrostatics?

Electrostatics is a branch of physics that studies the behavior of electrically charged particles at rest.

2. What is an electric field?

An electric field is a region of space around a charged particle or object in which a force is exerted on other charged particles.

3. How is an electric charge measured?

Electric charge is measured in units of coulombs (C) using an instrument called an electroscope.

4. What is the difference between conductors and insulators?

Conductors are materials that allow electricity to flow through them easily, while insulators are materials that do not allow electricity to flow through them easily.

5. What is Coulomb's law?

Coulomb's law states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

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