please check:
Two point charges, initially 1 cm apart, are moved to a distance of 3 cm apart. By what factor do the resulting electric and gravitational forces between them change?
a. 9
b. 3
c. 1/3
d. 1/9
D
Two positive charges, each of magnitude q, are on the y-axis at points y = +a and y = -a. Where would a third positive charge of the same magnitude be located for the net force on the third charge to be zero?
a. at the origin
b. at y = 2a
c. at y = -2a
d. at y = -a
A
Which is the MOST correct statement regarding the drawing of electric field lines?
a. electric field lines always connect from one charge to another
b. electric field lines always form closed loops
c. electric field lines can start on a charge of either polarity
d. electric field lines can never cross each other
D
correct
Bozo u are correct no need to check
To check the answers:
1. For the first question, the initial distance between the charges is 1 cm and the final distance is 3 cm. The electric force between two point charges is inversely proportional to the square of the distance between them (F ∝ 1/r^2). Therefore, when the distance is tripled (changed by a factor of 3), the electric force would decrease by a factor of (1/3)^2 = 1/9. The gravitational force between two point masses also follows the same inverse square law. So the factor by which the resulting electric and gravitational forces change is the same, which is 1/9. Thus, the correct answer is d. 1/9.
2. For the second question, if the net force on the third charge is zero, it means that the electric forces exerted by the two charges located at y = +a and y = -a cancel each other out. In order for this to happen, the third charge must be located on the x-axis, equidistant from the two charges. This point is the origin. Therefore, the correct answer is a. at the origin.
3. For the third question, let's evaluate the statements one by one:
a. Electric field lines do not always connect from one charge to another. They represent the direction of the electric field at each point in space.
b. Electric field lines do not always form closed loops. If there are no charges enclosed by the loop, the field lines should not form closed loops.
c. Electric field lines can start on a charge of either polarity. This statement is correct. Electric field lines start from positive charges and end on negative charges, or extend to infinity if there are no other charges.
d. Electric field lines can never cross each other. This statement is correct. Electric field lines cannot cross because the electric field at any point can only have one direction.
From the given options, the most correct statement is d. electric field lines can never cross each other.
To solve the given problems, we need to understand the concepts of electric and gravitational forces and field lines.
Problem 1:
The question asks about the change in electric and gravitational forces between two point charges when they are moved from a distance of 1 cm apart to 3 cm apart.
To find the factor by which the forces change, we need to apply the formulas for electric and gravitational forces and compare the values.
The electric force between two charges is given by Coulomb's Law:
\(F_e = \frac{k \cdot q_1 \cdot q_2}{r^2}\)
where \(F_e\) is the electric force, \(k\) is the electrostatic constant, \(q_1\) and \(q_2\) are the charges, and \(r\) is the separation distance.
The gravitational force between two masses is given by Newton's Law of Universal Gravitation:
\(F_g = \frac{G \cdot m_1 \cdot m_2}{r^2}\)
where \(F_g\) is the gravitational force, \(G\) is the gravitational constant, \(m_1\) and \(m_2\) are the masses, and \(r\) is the separation distance.
To find the factor by which the forces change, we need to calculate the ratio of the forces at the new distance (3 cm) to the forces at the initial distance (1 cm):
\(\mathrm{Factor} = \frac{{F_{\text{new}}}}{{F_{\text{initial}}}}\)
Let's calculate this ratio for both electric and gravitational forces:
Electric force ratio:
\(\frac{{F_{e, \text{new}}}}{{F_{e, \text{initial}}}} = \frac{{\frac{{k \cdot q_1 \cdot q_2}}{{(3 \,\text{cm})^2}}}}{{\frac{{k \cdot q_1 \cdot q_2}}{{(1 \,\text{cm})^2}}}} = \frac{{1 \,\text{cm}^2}}{{9 \,\text{cm}^2}} = \frac{1}{9}\)
Gravitational force ratio:
\(\frac{{F_{g, \text{new}}}}{{F_{g, \text{initial}}}} = \frac{{\frac{{G \cdot m_1 \cdot m_2}}{{(3 \,\text{cm})^2}}}}{{\frac{{G \cdot m_1 \cdot m_2}}{{(1 \,\text{cm})^2}}}} = \frac{{1 \,\text{cm}^2}}{{9 \,\text{cm}^2}} = \frac{1}{9}\)
By comparing the factors, we can see that both the electric and gravitational forces reduce by a factor of 1/9. Therefore, the answer is option d) 1/9.
Problem 2:
The question asks about the location for a third positive charge to have zero net force when two positive charges are placed on the y-axis at points y = +a and y = -a.
To find the location, we need to consider the forces exerted by the two charges on the third charge. Since the two charges are positive, they repel other positive charges.
At the origin (y = 0), the forces from the two charges will be equal in magnitude but opposite in direction. Thus, the net force on the third charge will be zero. Therefore, the answer is option a) at the origin.
Problem 3:
The question asks about the correct statement regarding the drawing of electric field lines.
Electric field lines represent the direction and strength of electric fields produced by charges. To understand the options, let's analyze each statement:
a) Electric field lines always connect from one charge to another.
This statement is incorrect. Electric field lines represent the direction of the electric field, not the connection between charges. They can start or end on charges or be continuous, depending on the configuration of charges.
b) Electric field lines always form closed loops.
This statement is incorrect. Electric field lines can be open or closed loops, depending on the configuration of charges. They are not always closed loops.
c) Electric field lines can start on a charge of either polarity.
This statement is correct. Electric field lines can start or end on charges of either positive or negative polarity. The lines originate from positive charges and terminate on negative charges, or vice versa.
d) Electric field lines can never cross each other.
This statement is correct. Electric field lines do not cross each other. If they were to cross, it would imply that the electric field has two different directions at the same point, which is not possible.
Based on the analysis, the MOST correct statement regarding the drawing of electric field lines is option d) electric field lines can never cross each other.
I hope this explanation helps! Let me know if you have any more questions.