The electric field 1.5 cm from a very small charged object points toward the object with a
magnitude of 180,000 N/C. What is the charge on the object?
To find the charge on the object, we can use Coulomb's law, which states that the electric field (E) created by a point charge is proportional to the charge (Q) and inversely proportional to the distance (r) squared. Mathematically, Coulomb's law is represented as:
E = k * (Q / r^2)
Where:
- E is the electric field magnitude (180,000 N/C)
- k is Coulomb's constant (9 x 10^9 N·m^2/C^2)
- Q is the charge on the object (unknown)
- r is the distance from the object (1.5 cm or 0.015 m)
By rearranging the equation, we can solve for Q:
Q = E * r^2 / k
Now, we can plug in the values and calculate the charge:
Q = (180,000 N/C) * (0.015 m)^2 / (9 x 10^9 N·m^2/C^2)
Q = 405 N·m^2/C
Therefore, the charge on the object is 405 coulombs.