39. The electrostatic force between two charged spheres is 64 N. What will the magnitude of the force be if the size of each charge is doubled and the distance between the spheres is doubled?
force = constant* charge1*charge2/distance^2
charge 1, charge 2 are doubled, and distance doubled
2*2/2^2=4/4 = 1, so it remains same.
Well, if the size of each charge is doubled, that means we're dealing with even bigger charges. It's like going from mini marshmallows to jumbo marshmallows - marshmallow madness!
Now, since the distance between the spheres is also doubled, it's like the marshmallows are trying to have a long-distance relationship. Calling it a "long-distance marsh-mance", if you will.
But let's get back to the question. To calculate the new force, we need to take into account the fact that the charge and distance have both changed.
If we double the charge, that means we're doubling the force. So, the new force will be 2 times the original force, which gives us 2 * 64 N = 128 N.
And since the distance between the spheres is also doubled, that means we need to divide the force by 2^2 (which is 4). So, the final answer is 128 N / 4 = 32 N.
So, the magnitude of the force will be 32 N. That's quite a shocker, isn't it? Electrifying, you might say!
To determine the new magnitude of the force, we can use Coulomb's Law, which states that the electrostatic force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Given:
Initial force (F₁) = 64 N
Charge 1 (Q₁) = Charge 2 (Q₂)
Distance 1 (d₁) = Distance 2 (d₂)
We need to find the new force (F₂) when the charge and distance are doubled.
Step 1: Write down Coulomb's Law formula:
F = (k * Q₁ * Q₂) / d²
Step 2: Calculate the constant k (Coulomb's constant):
k = 8.99 * 10^9 Nm²/C²
Step 3: Determine the proportionality factor between old and new forces:
(F₁ / F₂) = (Q₁ * Q₂) / (Q₁ * Q₂) * (d₁² / d₂²)
Step 4: Substitute the given values into the proportionality factor:
(64 / F₂) = (Q₁ * Q₂) / (Q₁ * Q₂) * (d₁² / d₂²)
Step 5: Substitute the doubled charges and distances:
(64 / F₂) = (2Q₁ * 2Q₂) / (Q₁ * Q₂) * (2d₁)² / (2d₂)²
Step 6: Simplify the equation:
64 / F₂ = 4 * (d₁ / d₂)²
Step 7: Substitute the given values:
64 / F₂ = 4 * (1 / 2)²
Step 8: Simplify the equation:
64 / F₂ = 4 * (1 / 4)
Step 9: Simplify further:
64 / F₂ = 1
Step 10: Solve for F₂:
F₂ = 64 N
Therefore, the new magnitude of the force when the size of each charge is doubled and the distance between the spheres is doubled is 64 N.
To find the solution to this problem, we need to break it down into steps:
Step 1: Understand the given information
We are given:
- The electrostatic force between two charged spheres is 64 N.
Step 2: Analyze the question
We need to determine the magnitude of the force when the size of each charge is doubled, and the distance between the spheres is doubled.
Step 3: Identify relevant principles/formulas
In electrostatics, the force between two charged objects can be calculated using Coulomb's Law:
F = k * (Q1 * Q2) / r^2
where F is the electrostatic force, k is the electrostatic constant (9 x 10^9 Nm^2/C^2), Q1 and Q2 are the charges of the two spheres, and r is the distance between them.
Step 4: Apply the principles/formulas to solve the problem
Let's assume:
- The initial charge of each sphere is Q.
- The initial distance between the spheres is r.
According to the question, when each charge is doubled, the new charges become 2Q. Similarly, when the distance between the spheres is doubled, the new distance becomes 2r.
Using Coulomb's Law, we can write the equation for the initial electrostatic force as:
64 = (k * (Q * Q)) / r^2
Now, let's find the new electrostatic force when the charges and distance are doubled:
F' = (k * ((2Q) * (2Q))) / (2r)^2
= (k * (4 * Q^2)) / (4 * r^2)
= (k * Q^2) / r^2
Step 5: Simplify the expression
Since k, Q, and r are the same in both cases, we can simplify the expression for the new electrostatic force as:
F' = 64 N
Step 6: Interpret the result
The magnitude of the force will remain the same (64 N) when the size of each charge is doubled and the distance between the spheres is doubled.
In summary, the magnitude of the force will be 64 N.