High School

The value of the electric field at a distance of 38.6 m from a point charge is 67.7 N/C and is directed radially in toward the charge. What is the charge? The Coulomb constant is 8.98755×10 9

N⋅m 2

/C 2

. Answer in units of C.

Answer :

To determine the charge of the point charge, we can use the formula for the electric field generated by a point charge:
Electric Field (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, and r is the distance from the point charge.

In this case, we have an electric field of 67.7 N/C at a distance of 38.6 m. Substituting these values into the formula, we can solve for q:
67.7 N/C = (8.98755 × 10^9 N·m^2/C^2 * q) / (38.6 m)^2.
Simplifying the equation, we find:
q = (67.7 N/C * (38.6 m)^2) / (8.98755 × 10^9 N·m^2/C^2).
Evaluating this expression, we can find the value of q in coulombs.

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