Question
Question: A combination of capacitors is set up as shown in the figure. The magnitude of the electric field du...
A combination of capacitors is set up as shown in the figure. The magnitude of the electric field due to a point charge Q (having a charge equal to sum of capacitance on 4μC and 9μC capacitors), at a point 30 m form it, would equal
A. 250 N/C
B. 360 N/C
C. 420 N/C
D. 480 N/C
Solution
While solving this question, try to solve each part one by one. By doing so will help make the diagram more simplified. Remember the additional rule of capacitors. Capacitors in parallel are added directly while those in series have to be added inversely.
Complete answer:
Let us solve the question by breaking the diagram
For the capacitors with capacitance 4μC, 3μC and 9μC, the system will be:
Since the capacitors with capacitance 3μC and 9μCare in parallel system,
The net charge will be the sum of their individual capacitance, i.e.,
⇒3μC+ 9μC=12μC
So now, the resultant system will be
Now,
The capacitors shown in the above figure will be in series
So, the net charge will be the sum of inverse of the capacitance
Hence, we have
⇒(41+121)−1=(31)−1=3μC
Now,
Total charge will be,
⇒Q=CV=3×8=24μC
This is the charge distributed by the direct ratio of capacitors 3μC and 9μC
So,
⇒Q9μF=3+324×9=18μC
Now,
Q9μF+Q4μF=18+24=42μC
So,
The magnitude of the electric field due to a point charge 42μC at a point 30 m form it, would equal
⇒E=r2kQ
⇒E=9009×109×42×10−6
⇒E=420N/C
So, The magnitude of the electric field due to a point charge Q (having a charge equal to the sum of capacitance on 4μC and 9μC capacitors), at a point 30 m from it, would equal 420 N/C.
So, the correct answer is “Option C”.
Note:
Remember the addition rule for the capacitors are opposite of those for the resistances. In the case of resistance, the resistance in parallel are added inversely while those in series are added directly. Also, always remember to change the units into the ones that are given in the option for finding the correct answer. For example in this question, the value that was given for the capacitors were on the micro scale. So,
1μC=10−6C