In this unit, you were learning about different yet similar laws of physics - Newton’s universal law of gravitation and Coulomb’s law of electrostatics. Describe one similarity and one difference for these two laws.
One similarity between Newton's law of gravitation and Coulomb's law of electrostatics is that both laws describe forces between objects based on their masses or charges, respectively.
However, a key difference between these laws is the nature of the force. In Newton's law of gravitation, the force is always attractive and depends on the product of the masses of the objects involved. On the other hand, in Coulomb's law of electrostatics, the force can be both attractive and repulsive and depends on the product of the charges of the objects involved.
Newton’s universal law of gravitation and Coulomb’s law of electrostatics. Describe one similarity and one difference for these two laws
One similarity between Newton's law of gravitation and Coulomb's law of electrostatics is that both laws describe inverse square relationships. In both laws, the force between two objects decreases with the square of the distance between them.
However, a key difference between these laws is the nature of the force and the properties of the objects involved. In Newton's law of gravitation, the force is always attractive and depends on the masses of the objects. On the other hand, in Coulomb's law of electrostatics, the force can be both attractive and repulsive and depends on the charges of the objects. Additionally, while gravity is always attractive and acts on all objects with mass, electrostatic forces only exist between objects with electric charge.
Refer to the following two images for the questions that follow.
A source charge with electric field lines radiating away from the source Two oppositely charged spheres are side by side with electric field lines surrounding both charges
Refer to Figure 1:
State whether the source charge is positively or negatively charged.
Figure 1 contains arrows that are outwardly pointing. By convention, state how the directions of field lines are detected.
Based on the description provided, the source charge in Figure 1 is positively charged.
In Figure 1, the arrows of the electric field lines are outwardly pointing. According to convention, this indicates that the electric field lines represent the direction a positive test charge would move if placed in the field.
Comparing Figure 1 and Figure 2, you can see Figure 2 does not have any arrowheads. Observe the sign of charges for each source charge, (in Figure 2) and state the direction the arrowheads should be pointing to make it accurate.
In Figure 2, the absence of arrowheads indicates that it is a diagram showing the electric field lines surrounding two oppositely charged spheres.
If the charges on the spheres are opposite as mentioned, the arrowheads on the electric field lines should point towards the positively charged sphere and away from the negatively charged sphere, in order for the diagram to accurately represent the electric field.
Examine the charge distribution in the diagram below. Illustration for the distribution of charges. Charge 1,2 and3 forma right triangle. Charge 1 and charge 2 form the base separated by 2.0 m. Charge 3 is directly above charge 1 separated by 2.0 m.
Determine the net force charge acting at q1 (+ 2.0 × 10-5
C), caused by q2 (-4.0 × 10-5
C) and q3 (-4.0 × 10-5
C). Be sure to include a free body diagram representing the force acting at q1 in your solution.
To determine the net force acting on q1, we need to calculate the individual forces between q1 and q2, as well as between q1 and q3, and then find the vector sum of these forces.
The force between two charges can be calculated using Coulomb's law:
F = (k * |q1| * |q2|) / r^2
Where F is the force between the charges, k is the Coulomb's constant (k = 9.0 x 10^9 Nm^2/C^2), |q1| and |q2| are the magnitudes of the charges, and r is the distance between the charges.
Given the magnitudes of the charges and the distance between them, we can calculate the forces:
Force between q1 and q2:
|q1| = 2.0 x 10^-5 C
|q2| = 4.0 x 10^-5 C (negative sign indicates opposite charges)
r = 2.0 m
Using Coulomb's law:
F12 = (9.0 x 10^9 Nm^2/C^2 * |2.0 x 10^-5 C| * |4.0 x 10^-5 C|) / (2.0 m)^2
= -36.0 N
The negative sign indicates that the force between q1 and q2 is attractive.
Force between q1 and q3:
|q1| = 2.0 x 10^-5 C
|q3| = 4.0 x 10^-5 C (negative sign indicates opposite charges)
r = 2.0 m
Using Coulomb's law:
F13 = (9.0 x 10^9 Nm^2/C^2 * |2.0 x 10^-5 C| * |4.0 x 10^-5 C|) / (2.0 m)^2
= -36.0 N
The negative sign indicates that the force between q1 and q3 is attractive.
Now, we can find the net force acting on q1 by taking the vector sum of F12 and F13. Since both forces have the same direction (toward q1), we can simply add their magnitudes:
Net force = |F12| + |F13|
= |-36.0 N| + |-36.0 N|
= 72.0 N
Therefore, the net force acting on q1 is 72.0 N, directed toward q1 as shown in the free body diagram.