The value of the electric field at a distance
of 86.9 m from a point charge is 74.9 N/C and
is directed radially in toward the charge.
What is the charge? The Coulomb constant
is 8.98755 × 109 N · m2
/C
2
.
Answer in units of C.
To find the charge, we can use Coulomb's law equation, which relates the electric field (E) to the charge (Q) and the distance (r):
E = k * Q / r^2
Where:
- E is the electric field
- k is the Coulomb constant (8.98755 × 10^9 N·m^2/C^2)
- Q is the charge
- r is the distance
In this case, we are given the electric field (E = 74.9 N/C) and the distance (r = 86.9 m), and we need to find the charge (Q).
Rearranging the equation, we can solve for Q:
Q = E * r^2 / k
Now, let's substitute the given values:
Q = 74.9 N/C * (86.9 m)^2 / (8.98755 × 10^9 N·m^2/C^2)
Calculating this expression:
Q = 136.733 C
Therefore, the value of the charge is approximately 136.733 Coulombs.