Question

The attractive electrostatic force between the point charges +8.44 ✕ 10-6 and q has a magnitude of 0.961 n when the separation between the charges is 0.67 m. find the sign and magnitude of the charge q.

Answer 1

To find the charge q, use Coulomb's law and solve for q2, considering that an attractive force implies opposite charges. The magnitude can be calculated by substituting the given values into the rearranged Coulomb's formula and accounting for the known charge, distance, and force.

Step-by-step explanation:

The question asks to find the sign and magnitude of charge q exerting an electrostatic force with another known charge. To solve this, we can use Coulomb's law, which states that the electrostatic force (F) between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. Using the formula F = k * |q1 * q2| / r^2, where k is Coulomb's constant (approximately 8.99 x 10^9 N·m²/C²), q1 is the known charge (+8.44 × 10^-6 C), q2 is the charge we're solving for, r is the separation distance between the charges (0.67 m), and F is the given force (0.961 N).

First, we isolate q2: q2 = F * r^2 / (k * q1). Plugging in the values, we get q2 = (0.961 N * (0.67 m)^2) / (8.99 x 10^9 N·m²/C² * 8.44 x 10^-6 C) to get the magnitude of q. As for the sign, since the force is attractive, the charges must be opposite in sign; thus, q will have negative polarity.

Answer 2

The electrostatic force between two charges Q1 and q is given by

`F=k_e (Q_1 q)/(r^2)`
where
ke is the Coulomb's constant
Q1 is the first charge
q is the second charge
r is the distance between the two charges

Re-arranging the formula, we have

`q= (F r^2)/(k_e Q_1)`
and since we know the value of the force F, of the charge Q1 and the distance r between the two charges, we can calculate the value of q:

`q= ((0.961 N)(0.67 m)^2)/((8.99 \cdot 10^9 N m^2 C^(-2))(+8.44\cdot 10^(-6)C))=5.69 \cdot 10^(-6) C`

And since the force is attractive, the two charges must have opposite sign, so the charge q must have negative sign.