two charges repel each other with a force of 0.1N when they are 5cm apart. Find the forces between the same charges when they are 2cm and 8cm apart.

F= 0.1N

r1= 5 cm
= 0.05m
r2= 4 cm
= 0.04m
F= k(q1 q2)/r2 eq 1
k(q1 q2)= F*r2 put in equation 2
F'=k(q1 q2)/r'2 eq 2
F'=F*r2/r'2
Putting values
F'= 0.1*(0.05)*(0.05)/(0.04)*(0.04)
F'=0.62N

Force of repulsion =F=0.1 N

Distance between two charges =r=5cm=0.05m
Both charges are identical.
Force of same charges when r =2cm=0.02m
F=k×(q1q2)÷r2(whole square)
By using coulombs law we know that;
F=k×(q1q2)÷r2(whole square)
Since;it is provided that q1=q2=q
Hence we can write it as;
F=k(q)2(whole square)÷r2(whole square)
When distance =5cm
Foce F1=k(q)2(whole square)÷(0.05)2(whole square)=0.1 eq 1
When distance is 2cm
=0.02m,F2=?
F2=k(q)2(whole square)÷(0.02)2(whole square) eq 2
Dividing equation 2 by 1
F2÷0.1=(0.05)(0.05)÷(0.02)(0.02)=25÷4
F2=25÷4×0.1=0.62N
F2=0.62N

0.62N

Why did the charges go on a distance spree? Because they couldn't keep their attraction and repulsion under control! All right, let's tackle this electrifying question.

We can use Coulomb's law, which states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

Given that the force between the charges is 0.1N at a distance of 5cm, we can set up the following equation:

0.1N = k * (q1 * q2) / (0.05m)^2

Now, let's find the value of k (Coulomb's constant). Its value is approximately 9 x 10^9 Nm^2/C^2.

Plugging in the values, we have:

0.1N = (9 x 10^9 Nm^2/C^2) * (q1 * q2) / (0.05m)^2

Simplifying this equation, we get:

(q1 * q2) = (0.1N * (0.05m)^2) / (9 x 10^9 Nm^2/C^2)

Now that we have the product of the charges, we can calculate the forces at different distances.

For a distance of 2cm (0.02m):

Force = (9 x 10^9 Nm^2/C^2) * [(q1 * q2) / (0.02m)^2]

For a distance of 8cm (0.08m):

Force = (9 x 10^9 Nm^2/C^2) * [(q1 * q2) / (0.08m)^2]

Remember, charges are quite mercurial. They can attract or repel depending on their signs. So, pay attention to the signs of the charges when calculating the forces!

To find the forces between the same charges when they are 2cm and 8cm apart, we need to use Coulomb's Law. Coulomb's Law states that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.

The formula for Coulomb's Law is:

F = (k * q1 * q2) / r^2

Where:
F is the force between the charges,
k is the Coulomb's constant (approximately 9 x 10^9 Nm^2/C^2),
q1 and q2 are the magnitudes (values) of the charges,
r is the distance between the charges.

Let's calculate the forces for the given distances.

When the charges are 5cm apart:
F1 = 0.1N

Now, let's calculate F2 when the charges are 2cm apart:
r2 = 2cm = 0.02m

F2 = (k * q1 * q2) / r2^2

We know that F1 = F2, which means:

0.1N = (k * q1 * q2) / r2^2

Let's rearrange the equation to solve for F2:

F2 = F1 * (r2^2 / r1^2)

F2 = 0.1N * (0.02^2 / 0.05^2)

Now, let's calculate F2:

F2 = 0.1N * (0.0004 / 0.0025)

F2 ≈ 0.016N

So, when the charges are 2cm apart, the force between them is approximately 0.016N.

Similarly, let's calculate F3 when the charges are 8cm apart:
r3 = 8cm = 0.08m

F3 = (k * q1 * q2) / r3^2

We know that F1 = F3, which means:

0.1N = (k * q1 * q2) / r3^2

Let's rearrange the equation to solve for F3:

F3 = F1 * (r3^2 / r1^2)

F3 = 0.1N * (0.08^2 / 0.05^2)

Now, let's calculate F3:

F3 = 0.1N * (0.0064 / 0.0025)

F3 ≈ 0.256N

So, when the charges are 8cm apart, the force between them is approximately 0.256N.

Therefore, the forces between the same charges when they are 2cm and 8cm apart are approximately 0.016N and 0.256N, respectively.