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Two spheres 4cm apart, attract each other with a force of 1.2×10^9N. Determine the magnitude of the charge on each tosee if one has two the charge (of the opposite sign) as the other?

Mar 13

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Mar 13

To determine the magnitude of the charge on each sphere, we can use Coulomb's Law:

F = k * (q1 * q2) / r^2

Where:

F = force between the spheres (1.2×10^9N)

k = Coulomb's constant (8.99 x 10^9 N m^2/C^2)

q1 and q2 = charges on the spheres

r = distance between the spheres (4cm = 0.04m)

Plugging in the values:

1.2×10^9N = (8.99 x 10^9 N m^2/C^2) * (q1 * q2) / (0.04m)^2

1.2×10^9N = (8.99 x 10^9 N m^2/C^2) * (q1 * q2) / 0.0016m^2

1.2×10^9N = 5.61875 x 10^12 * q1 * q2

q1 * q2 = 1.2×10^9N / 5.61875 x 10^12

q1 * q2 = 0.2134 x 10^-3

Since we are looking for the magnitude of the charge on each sphere, we can assume that one charge is positive and the other is negative. Therefore, we can write:

q1 = q

q2 = -q

Substitute these values into the equation:

q * -q = 0.2134 x 10^-3

-q^2 = 0.2134 x 10^-3

q^2 = -0.2134 x 10^-3

q = sqrt(-0.2134 x 10^-3)

q = 0.462 C

Therefore, the magnitude of the charge on each sphere is 0.462 C. This means that one sphere has twice the charge (of the opposite sign) as the other.

F = k * (q1 * q2) / r^2

Where:

F = force between the spheres (1.2×10^9N)

k = Coulomb's constant (8.99 x 10^9 N m^2/C^2)

q1 and q2 = charges on the spheres

r = distance between the spheres (4cm = 0.04m)

Plugging in the values:

1.2×10^9N = (8.99 x 10^9 N m^2/C^2) * (q1 * q2) / (0.04m)^2

1.2×10^9N = (8.99 x 10^9 N m^2/C^2) * (q1 * q2) / 0.0016m^2

1.2×10^9N = 5.61875 x 10^12 * q1 * q2

q1 * q2 = 1.2×10^9N / 5.61875 x 10^12

q1 * q2 = 0.2134 x 10^-3

Since we are looking for the magnitude of the charge on each sphere, we can assume that one charge is positive and the other is negative. Therefore, we can write:

q1 = q

q2 = -q

Substitute these values into the equation:

q * -q = 0.2134 x 10^-3

-q^2 = 0.2134 x 10^-3

q^2 = -0.2134 x 10^-3

q = sqrt(-0.2134 x 10^-3)

q = 0.462 C

Therefore, the magnitude of the charge on each sphere is 0.462 C. This means that one sphere has twice the charge (of the opposite sign) as the other.