Question

Two objects, A with charge +Q and B with charge +4Q, are separated by a distance r. The magnitude of the force exerted on the second object by the first is F. If the first object is moved to a distance 2r from the second object, what is the magnitude of the electric force on the second object?

Answer 1

The magnitude of the electric force on the second object remains the same when the first object is moved to a distance 2r from it.

Step-by-step explanation:

To find the magnitude of the electric force on the second object (B) when the first object (A) is moved to a distance 2r from B, we can use Coulomb's law. Coulomb's law states that the magnitude of the electric 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 that the charge of A is Q and the charge of B is 4Q, the force exerted on B when A is at distance r is F. Now, when A is moved to a distance 2r from B, the new distance between A and B is 2r. Using Coulomb's law and the proportionalities mentioned earlier, the magnitude of the new electric force on B can be calculated as:

F' = (k * Q * 4Q) / (2r)^2

Where k is the constant in Coulomb's law. Simplifying the equation gives:

F' = (4 * F) / 4 = F

Therefore, the magnitude of the electric force on the second object B remains the same when the first object A is moved to a distance 2r from B.

Answer 2

The magnitude of electric force on object B due to object A when they are 2r distance apart is F/4.

Step-by-step explanation:

Given :

Electric charge on object A = +Q

Electric charge on object B = +4Q

When the objects A and B are r distance apart, the magnitude of electrostatic force exerted on B due to A is given by the relation :

`F=(1)/(4\pi\epsilon_(0) ) (Q*4Q)/(r^(2) )` .....(1)

Now, the two objects are apart by distance of 2r, hence the force acting on the object B due to A is :

`F_(1) =(1)/(4\pi\epsilon_(0) ) (Q*4Q)/((2r)^(2) )`

`F_(1) =(1)/(4\pi\epsilon_(0) ) (Q*4Q)/(4r^(2) )`

Substitute equation (1) in the above equation.

`F_(1) =(F)/(4)`