Objects A and B are both positively charged. Both have a mass of 100 g, but A has twice the charge of B. When A and B are placed 10 cm apart, B experiences an electric force of 0.45 N. What is the charge on A?

Verified step by step guidance

1. Step 1: Start by identifying the relevant formula for the electric force between two charges. The formula is Coulomb's Law: $F\; =\; k\; *\; (q\_1\; *\; q\_2)\; /\; r^2$, where F is the electric force, k is Coulomb's constant ($8.99\; \times \; 10^9\; \backslash ,\; N\; \backslash ,\; m^2\; /\; C^2$), $q\_1$ and $q\_2$ are the charges, and r is the distance between the charges.
2. Step 2: Assign the given values to the variables. The force $F$ is 0.45 N, the distance $r$ is 10 cm (convert to meters: $r\; =\; 0.1\; \backslash ,\; m$), and the relationship between the charges is $q\_A\; =\; 2q\_B$.
3. Step 3: Substitute $q\_A\; =\; 2q\_B$ into Coulomb's Law. The equation becomes: $F\; =\; k\; *\; (2q\_B\; *\; q\_B)\; /\; r^2$, which simplifies to $F\; =\; k\; *\; (2q\_B^2)\; /\; r^2$.
4. Step 4: Rearrange the equation to solve for $q\_B$. The equation becomes: $q\_B^2\; =\; (F\; *\; r^2)\; /\; (2k)$. Take the square root to find $q\_B$: $q\_B\; =\; sqrt((F\; *\; r^2)\; /\; (2k))$.
5. Step 5: Once $q\_B$ is calculated, use the relationship $q\_A\; =\; 2q\_B$ to find the charge on A. This completes the solution.

Key Concepts

Coulomb's Law

Coulomb's Law describes the electrostatic force between two charged objects. It states that the force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This law is fundamental for calculating the electric force acting between charged objects, which is essential for solving the problem at hand.

Electric Charge

Electric charge is a property of matter that causes it to experience a force when placed in an electromagnetic field. Charges can be positive or negative, and like charges repel while opposite charges attract. In this scenario, understanding the relationship between the charges of objects A and B is crucial for determining the charge on A based on the given force experienced by B.

Force Calculation

The calculation of force in physics often involves using formulas that relate mass, acceleration, and in this case, electric force. For charged objects, the force can be calculated using Coulomb's Law. Knowing the force experienced by B allows us to backtrack and find the charge on A, given that A has twice the charge of B.