The respective charges on three identical metal spheres (q1, q2 and q3) are ̶ 16.9 µ C,
5.60 µ C and 2.6 µ C. The spheres are brought together so that they touch each other,
and are then separated and placed on the x and y axes.
Calculate the net electrostatic force exerted on the sphere that is located at the origin
q1 is at origin, q2 is at (5.3mm,0), q3 is at (0,5.3mm)
charge on each after touching =1/3 (-16.9+5.6+2.6)e-6 C = Q
so now, you have two forces (q1q2, q1,q3) at right angles
force from each: kQ^2/.0053^2
so the net force (right angles) is sqrt(2F^2)=Fsqrt2=kQ^2/.0053^2 * sqrt2
To calculate the net electrostatic force exerted on the sphere located at the origin, we need to consider the electrostatic forces between each pair of spheres. The formula for the electrostatic force between two charged objects is given by Coulomb's Law:
F = k * (|q1| * |q2|) / r^2
Where:
- F is the electrostatic force between the two charges.
- k is the electrostatic constant, which is approximately equal to 9 x 10^9 N m^2/C^2.
- |q1| and |q2| are the magnitudes of the charges.
- r is the distance between the centers of the spheres.
First, let's calculate the distances between the spheres:
- The distance between the origin and (5.3mm, 0) is equal to 5.3mm.
- The distance between the origin and (0, 5.3mm) is also equal to 5.3mm.
Now, let's calculate the electrostatic forces between each pair of spheres:
- Force between sphere q1 and q2:
F12 = k * (|q1| * |q2|) / r^2
= (9 x 10^9 N m^2/C^2) * (16.9 µC) * (5.60 µC) / (5.3mm)^2
- Force between sphere q1 and q3:
F13 = k * (|q1| * |q3|) / r^2
= (9 x 10^9 N m^2/C^2) * (16.9 µC) * (2.6 µC) / (5.3mm)^2
- Force between sphere q2 and q3:
F23 = k * (|q2| * |q3|) / r^2
= (9 x 10^9 N m^2/C^2) * (5.60 µC) * (2.6 µC) / (5.3mm)^2
Now, we can calculate the net electrostatic force by summing up the forces between each pair of spheres. Since forces are vectors, we need to consider both magnitude and direction:
Net Force = F12 + F13 + F23
To find the direction of the net force, we need to consider the distances and positions of the spheres. Since q2 is located at (5.3mm, 0) and q3 is located at (0, 5.3mm), the electric forces generated by q2 and q3 will have components in the x and y directions. We need to calculate the net forces in both directions separately.
Finally, by considering the magnitude and direction of the net force in the x and y directions, we can determine the overall net force on the sphere at the origin.