GuaSS law Might be Helpfull Here..!!
Consider two charges
and
. An electrostatic electric field line exits the positive charge
at 36 degrees and enters the negative charge
at 180 degrees, as shown in the figure above. What is the magnitude of ratio of charges
?
Details and Assumptions
- Use
- The given figure is a rough idea for this problem (Plz feel it), and sorry for inconvenient figure.
- This is not original Question
The answer is 10.47.
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I didn't use Gauss's law directly.
It's intuitive that Q is greater in magnitude than -q.
Now, only question that remains is how much.
since all of electric field lines of -q will be outnumbered by field lines of Q, and we know that total field lines of -q will be equal to field lines exiting Q which are contained in the shape of a cone with apex angle 2*36 degree, or pi/5.
that is because the field line which we are given information about completely encloses all field lines of -q.
I just calculated ratio of solid angle of unit sphere(4*pi) divided by the solid angle subtended by this cone on unit sphere. you can look up general formula for solid angle subtended by cone on wikipedia and convert it from a function of cos(x) to a function of sin(x/2) and you are done after putting x/2=pi/10 and sin(pi/10)=0.309.
The answer is 1/(0.309*0.309)=10.47.