Q. A charge of +3μC is placed in a uniform electric field of strength 1500 N/C. What is the work done in moving the charge 0.2 m in the direction of the field?
A.
90 J
B.
60 J
C.
30 J
D.
45 J
Solution
Work done W = F * d = (E * q) * d = (1500 N/C * 3 × 10^-6 C) * 0.2 m = 0.0009 J = 90 J.
Q. A charge Q is uniformly distributed over a spherical surface of radius R. What is the electric field at a point outside the sphere at distance r from the center?
A.
0
B.
Q/4πε₀r²
C.
Q/4πε₀R²
D.
Q/4πε₀R
Solution
For points outside the sphere, the electric field behaves as if all the charge were concentrated at the center, so E = Q/4πε₀r².
Q. A charged particle moves from a point of higher electric potential to a point of lower electric potential. What happens to its kinetic energy?
A.
Increases
B.
Decreases
C.
Remains constant
D.
Cannot be determined
Solution
As the charged particle moves to a lower potential, it loses potential energy, which is converted into kinetic energy, thus increasing its kinetic energy.
Q. A charged particle moves from a region of high potential to low potential. What happens to its kinetic energy?
A.
It increases
B.
It decreases
C.
It remains constant
D.
It becomes zero
Solution
As the charged particle moves from high potential to low potential, it loses potential energy, which is converted into kinetic energy, thus its kinetic energy increases.
Q. A charged sphere has a radius R and a total charge Q. What is the electric potential at a point outside the sphere at a distance r from the center (r > R)?
A.
kQ/R
B.
kQ/r
C.
kQ/(R+r)
D.
0
Solution
For a charged sphere, the electric potential outside the sphere behaves as if all the charge were concentrated at the center, so V = kQ/r.
Q. A cylindrical conductor of radius R carries a uniform charge per unit length λ. What is the electric field at a distance r from the axis of the cylinder (r > R)?
A.
0
B.
λ/(2πε₀r)
C.
λ/(2πε₀R)
D.
λ/(4πε₀r²)
Solution
For a point outside the cylinder, the electric field is given by E = λ/(2πε₀r).
Q. A cylindrical Gaussian surface encloses a charge Q. If the height of the cylinder is doubled while keeping the radius constant, what happens to the electric flux through the curved surface?
A.
It doubles
B.
It halves
C.
It remains the same
D.
It becomes zero
Solution
The electric flux through the curved surface is proportional to the charge enclosed, which remains constant, so the flux through the curved surface doubles if the height is doubled.
Q. A cylindrical Gaussian surface encloses a charge Q. If the radius of the cylinder is r and its height is h, what is the electric flux through the curved surface?
A.
Q/ε₀
B.
Q/(2ε₀)
C.
Q/(4ε₀)
D.
0
Solution
The electric flux through the curved surface of a cylinder is given by Φ = Q_enc/ε₀, where Q_enc = Q.
Q. A cylindrical Gaussian surface of length L and radius R encloses a charge Q uniformly distributed along its length. What is the electric field at a distance R from the axis of the cylinder?
A.
Q/(2πε₀R)
B.
Q/(4πε₀R²)
C.
0
D.
Q/(ε₀L)
Solution
Using Gauss's law, the electric field outside the cylinder is E = Q/(2πε₀R).
Q. A cylindrical Gaussian surface of length L and radius R encloses a charge Q. What is the electric field E at a distance R from the axis of the cylinder?
A.
Q/(2πε₀R)
B.
Q/(4πε₀R²)
C.
Q/(ε₀L)
D.
0
Solution
Using Gauss's law, the electric field E at a distance R from the axis of a long charged cylinder is E = Q/(2πε₀L) for points outside the cylinder.
Electrostatics is a crucial topic in physics that deals with the study of electric charges at rest. Understanding electrostatics is essential for students preparing for school exams and competitive tests, as it forms the foundation for many advanced concepts in physics. Practicing MCQs and objective questions on electrostatics not only enhances conceptual clarity but also boosts your confidence in tackling important questions during exams.
What You Will Practise Here
Fundamental concepts of electric charge and its properties
Understanding Coulomb's Law and its applications
Electric field and electric potential: definitions and calculations
Capacitance and capacitors: types and formulas
Gauss's Law and its significance in electrostatics
Concept of electric dipoles and their behavior in electric fields
Key diagrams and graphical representations related to electrostatics
Exam Relevance
Electrostatics is a significant topic in various exams, including CBSE, State Boards, NEET, and JEE. It frequently appears in the form of conceptual questions, numerical problems, and application-based scenarios. Students can expect to encounter questions that require them to apply Coulomb's Law, calculate electric fields, and analyze capacitor circuits. Familiarity with common question patterns will greatly aid in effective exam preparation.
Common Mistakes Students Make
Confusing the concepts of electric field and electric potential
Misapplying Coulomb's Law in multi-charge systems
Neglecting the direction of electric field lines in problem-solving
Overlooking the significance of units and dimensions in calculations
Failing to understand the behavior of capacitors in series and parallel
FAQs
Question: What is the difference between electric field and electric potential? Answer: The electric field is a vector quantity that represents the force experienced by a unit positive charge, while electric potential is a scalar quantity that indicates the potential energy per unit charge at a point in an electric field.
Question: How do capacitors store energy? Answer: Capacitors store energy in the form of an electric field created between their plates when a voltage is applied across them.
Now is the time to strengthen your understanding of electrostatics! Dive into our practice MCQs and test your knowledge on this vital topic. The more you practice, the better prepared you will be for your exams!
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