Two charges of # -4 C # and # -3 C# are positioned on a line at points # -8 # and # 16 #, respectively. What is the net force on a charge of # 2 C# at # -1 #?

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Answer 1 · 2015-12-24T15:05:03

No units are given for distance so I have assumed they are in metres for which:

#F=-1.28xx10^(9)"N"#

MFDocs

The force between two charges #q_1# and #q_2# separated by a distance #r# is given by Coulombs' Law:

#F=1/(4piepsilon_0).(q_1q_2)/r^2#

This simplifies down to:

#F=k.(q_1q_2)/r^2#

#k=9xx10^(9)"m""/""F"# and is the constant of proportionality.

The net force on #q_2# will be the vector sum of the other two forces:

#F_(res)=-F_(12)+F_(32)#

#=-k(4xx2)/7^2+k(3xx2)/17^2#

#=k(6/289-8/49)#

#=-kxx0.1423#

#F_(res)=-9xx10^(9)xx0.1423=-1.28xx10^(9)"N"#

The size of the force reflects how large a unit the coulomb is.