Two charges separated by one meter exert 1 Newton forces on each other. If the magnitude of each charge is doubled, the force on each charge is ______ Newtons.
Thanks!
4 times bigger - so I think the answer would be 4 Newtons.
4 newtons
69 hehe
Well, since the magnitude of each charge is doubled, we can say that the force of the "charge of the light brigade" will also double. So, the force on each charge will be 2 Newtons. Double the charge, double the fun!
To find the force on each charge when the magnitude of each charge is doubled, we can use Coulomb's Law. Coulomb's Law states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
Let's break down the steps to find the force:
Step 1: Determine the initial force between the charges.
Given that the charges are separated by one meter and exert a force of 1 Newton on each other, we can substitute these values into Coulomb's Law equation:
F = k * (q1 * q2) / r^2
Where F is the force, k is the electrostatic constant, q1 and q2 are the charges, and r is the distance between the charges.
Since the force is 1 Newton and the distance is 1 meter, we can simplify the equation:
1 = k * (q1 * q2) / 1^2
Step 2: Find the value of k.
The electrostatic constant, also known as Coulomb's constant, is approximately equal to 8.99 x 10^9 Nm^2/C^2.
Step 3: Calculate the product of the charges.
By rearranging the equation and substituting the known values, we can solve for the product of the charges:
(q1 * q2) = F * r^2 / k
(q1 * q2) = 1 * 1^2 / (8.99 x 10^9)
Step 4: Double the magnitude of each charge.
If we double the magnitude of each charge, we can multiply the original charges by 2:
(q1 * q2) = (2 * q1) * (2 * q2)
(q1 * q2) = 4 * (q1 * q2)
Step 5: Calculate the new force.
Substituting the new charges (4 * (q1 * q2)) into Coulomb's Law equation, we get:
F_new = k * (4 * (q1 * q2)) / r^2
F_new = 4 * (k * (q1 * q2) / r^2)
Step 6: Substitute the value of k and simplify the equation.
Since we know the value of k is 8.99 x 10^9 Nm^2/C^2, we can substitute it into the equation:
F_new = 4 * (8.99 x 10^9) * (q1 * q2) / r^2
F_new = 35.96 x 10^9 * (q1 * q2) / r^2
Therefore, when the magnitude of each charge is doubled, the force on each charge is 35.96 x 10^9 times the product of the charges / r^2 Newtons.
Coulomb's Law is:
F = kQ1*Q2 / d^2
k is a constant
Let's represent each charge as "q"
then the intial force F1 is:
F1 = k*q*q / 1^2 = kq^2
doubling the charge, the new force, F2, is:
F2 = k(2q)(2q) / 1^2 = 4kq^2
F2 is how many times bigger than F1?