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Two identical conducting spheres ( of negligible radius) I having charge of of opposite sign, I attract each other with a force of 0.108 N when separated by 0.5 meter. The sphere are connected by a conducting wire which is then removed when charge stops flowing and thereafter repel each other with a force of 0.036 N keeping the distance same. I What were the initial charges on the sphere?
Ref: https://edurev.in/question/495365/Two-identical-conducting-spheres-of-negligible-radius-I-having-charge-of-of-opposite-sign-I-attr

Here,
F1 = 0.108 N
r = 0.5 m
F2 = 0.036 N
let charges on the spheres be q1 and q2 respectively.
charges after connection gets redistributed in the spheres , so let charge on each sphere be q.
from conservation of charge
q1 + q2 = 2q...........eq.1

again
F1 = k q1q2/r²...........eq.2
F2 = k q²/r².............eq.3

=> 0.036 = 9×10⁹ ×q²/(0.5)²
=> q² = 0.036 × (0.5)²/9×10⁹
=> q² = 1×10⁻¹²
=> q=1×10⁻⁶ C.............eq.4

from eq 2 and 3
F1/F2 = q1q2/q²
=> 3 = q1q2/q²
3q² = q1q2
=> q1q2 = 3q²

again,

(q1 ₋ q2)² = (q1 + q2)² ₋ 4q1q2
 = (2q)² ₋ 3q²/r²
 = q²/r²

by eq.4
(q1₋q2) = q/r
=1×10⁻⁶/0.5
=2×10⁻⁶..............eq.5
from eq.1 and eq.4
q1 + q2 = 4×10⁻⁶..............eq.6
adding 5 and 6
q1 = 3×10⁻⁶
q1 = 3μC
subtracting 5 from 6
q2 = 1×10⁻⁶
q2 = 1μC

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Ans. The JEE exam, also known as the Joint Entrance Examination, is of utmost importance for students aspiring to pursue undergraduate programs in engineering or architecture in prestigious institutions in India. The exam serves as a gateway to renowned institutes like the Indian Institutes of Technology (IITs), National Institutes of Technology (NITs), and other government-funded technical institutions. It is highly competitive and plays a crucial role in determining admission to these esteemed institutions.
2. How can I prepare effectively for the JEE exam?
Ans. Effective preparation for the JEE exam requires a disciplined and strategic approach. Here are a few tips to enhance your preparation: - Understand the exam pattern and syllabus thoroughly. - Create a study schedule and allocate sufficient time for each subject. - Practice solving previous years' question papers and sample papers. - Seek guidance from experienced mentors or join coaching institutes if necessary. - Regularly revise concepts and formulas to strengthen your understanding. - Stay updated with current affairs and the latest developments in the field of science and technology. - Take mock tests to assess your progress and identify areas that need improvement. - Stay focused, motivated, and maintain a healthy balance between studies and recreation.
3. Are there any specific books recommended for JEE exam preparation?
Ans. Yes, there are several books that are highly recommended for JEE exam preparation. Some popular ones include: - Physics: Concepts of Physics by H.C. Verma, Problems in General Physics by I.E. Irodov, Fundamentals of Physics by Halliday, Resnick, and Walker. - Chemistry: Organic Chemistry by Morrison and Boyd, Physical Chemistry by O.P. Tandon, Inorganic Chemistry by J.D. Lee. - Mathematics: Higher Algebra by Hall and Knight, Coordinate Geometry by S.L. Loney, Problems in Calculus of One Variable by I.A. Maron. However, it is important to note that while these books provide comprehensive coverage, they should be used in conjunction with the NCERT textbooks and regular classroom notes. Additionally, it is advisable to refer to the specific recommendations of your coaching institute or mentor.
4. Is it possible to crack the JEE exam without joining a coaching institute?
Ans. Yes, it is possible to crack the JEE exam without joining a coaching institute. Many students have successfully cleared the exam through self-study and dedicated preparation. However, it requires a disciplined approach, consistent effort, and effective utilization of available resources. Here are a few tips for self-study: - Understand the exam pattern and syllabus thoroughly. - Make use of online resources, video lectures, and study materials available on educational websites. - Join online forums or study groups to clarify doubts and discuss concepts. - Solve previous years' question papers and take online mock tests to assess your progress. - Seek guidance from experienced teachers or mentors in case of doubts or difficulties. - Stay motivated, maintain a positive mindset, and follow a well-structured study schedule. While coaching institutes provide structured guidance and support, self-study can be equally effective if done with dedication and proper planning.
5. Can I take the JEE exam multiple times?
Ans. Yes, you can take the JEE exam multiple times. The JEE Main exam, which is the first stage of the JEE, is conducted twice a year by the National Testing Agency (NTA). Candidates can appear for both attempts in the same academic year and the best score out of the two attempts is considered for admission purposes. However, the JEE Advanced exam, which is the second stage of the JEE, can only be attempted twice in consecutive years. It is crucial to check the eligibility criteria and guidelines provided by the conducting authority for each attempt.
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