(a) What magnitude point charge creates a 20000 N/C electric field at a distance of 0.210 m?
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To find the magnitude of the point charge that creates a specific electric field, we can use the formula for electric field strength:
E = k * q / r^2
where:
E is the electric field strength in N/C,
k is the electrostatic constant (9.0 * 10^9 N m^2 / C^2),
q is the magnitude of the point charge,
r is the distance from the point charge.
In this case, we are given:
E = 20000 N/C
r = 0.210 m
k = 9.0 * 10^9 N m^2 / C^2
Now, we can rearrange the formula and solve for q:
q = E * r^2 / k
Substituting the given values and calculating:
q = (20000 N/C) * (0.210 m)^2 / (9.0 * 10^9 N m^2 / C^2)
Evaluating the expression:
q = (20000 N/C) * (0.0441 m^2) / (9.0 * 10^9 N m^2 / C^2)
q = 0.0882 C
Therefore, a point charge with a magnitude of 0.0882 C will create a 20000 N/C electric field at a distance of 0.210 m.