The distance from a point charge is tripled. What is the ratio of the strength of the electric field at the original distance to the strength of the field at the new distance?
a) 9:1
b) 3:1
c) 1:3
d) 1:9
Explanation
The strength of the electric field due to a point charge is given by the relationship: E=kq/r2. If E is the strength of the field at the original location, E’=kq/(3r)2=kq/(9r2). E’=E/9, i.e. E=9E’, and the ratio of the strength of the electric field at the original location to the strength at 3x the distance is 9:1.
a) 9:1, correct.
b) 3:1, incorrect, This would be true only if the E was inversely proportional to the distance, but E is inversely proportional to the distance squared.
c) 1:3, incorrect, This would be true if E was proportional to the distance, but E is inversely proportional to the distance squared.
d) 1:9, incorrect, This would only be true if E was proportional to the distance squared, but E is inversely proportional to the distance squared.
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