Two tiny conducting spheres are identical and carry charges of -18.1C and +47.4C. They are separated by a distance of 3.55 cm. (a) What is the magnitude of the force that each sphere experiences? (b) The spheres are brought into contact and then separated to a distance of 3.55 cm. Determine the magnitude of the force that each sphere now experiences.
To find the magnitude of the force between the two conducting spheres, we can use Coulomb's law. Coulomb's law states that the 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.
(a) To find the magnitude of the force before the spheres are brought into contact, we can use the formula:
\[ F = \frac{k \cdot |Q_1 \cdot Q_2|}{r^2} \]
Where:
- F is the magnitude of the force
- k is the electrostatic constant with a value of 9 x 10^9 N m^2/C^2
- |Q1 × Q2| is the product of the charges, taking the absolute value to ignore the sign
- r is the distance between the spheres
Plugging in the values:
- |Q1| = 18.1 C
- |Q2| = 47.4 C
- r = 3.55 cm (converting to meters by dividing by 100)
We can now calculate the magnitude of the force using the formula.
(b) After bringing the spheres into contact, their charges equalize due to the transfer of electrons. Since the spheres are identical, they will have the same final charge. The total charge will be the sum of the initial charges: -18.1 C + 47.4 C = 29.3 C.
Now, we need to calculate the magnitude of the force after the spheres are separated to a distance of 3.55 cm again. We can use the same formula as before, but this time with the total charge of 29.3 C for both spheres.
Plugging in the values:
- |Q1| = 29.3 C (total charge after contact)
- |Q2| = 29.3 C (total charge after contact)
- r = 3.55 cm (converting to meters by dividing by 100)
Finally, we can calculate the magnitude of the force after the spheres are separated using the formula.
Following these steps, you should be able to find the answers to both parts of the question.