To calculate the value of Q in the given scenario, we can use the equation for the electric force between two charged objects:
Fe = k * |Q1 * Q2| / r^2
Where:
- Fe is the electric force between the objects
- k is the electrostatic constant (in our universe, it is approximately 9 x 10^9 N m^2/C^2)
- Q1 and Q2 are the charges of the objects
- r is the distance between the objects
In the given scenario, the electric attraction between the sun and the earth replaces the gravitational force. Since the earth is in orbit, the electric force is equal to the centripetal force needed to keep the earth in its orbit. The centripetal force is given by:
Fc = (m * v^2) / r
Where:
- Fc is the centripetal force
- m is the mass of the earth
- v is the orbital velocity of the earth
- r is the orbital radius
In both universes (our universe and the hypothetical parallel universe), the mass, orbital radius, and orbital period are the same for the earth. Therefore, the only difference is the type of force involved—gravity in our universe and electric force in the parallel universe.
To equate the electric force and the centripetal force in the parallel universe, we can set them equal to each other:
Fe = Fc
Then plug in the respective equations:
k * |Q1 * Q2| / r^2 = (m * v^2) / r
Since the earth carries charge -Q and the sun carries charge Q:
k * |-Q * Q| / r^2 = (m * v^2) / r
Now we can simplify the equation:
k * Q^2 / r^2 = m * v^2 / r
Solving for Q:
Q^2 = (m * v^2 * r) / (k * r^2)
Q^2 = (m * v^2) / (k * r)
Q = √[(m * v^2) / (k * r)]
To find the value of Q, we need to know the values of m (mass of the earth), v (orbital velocity of the earth), r (orbital radius), and k (the electrostatic constant). Since these values are not provided in the given question, we are unable to perform the calculation to find the value of Q.