CBSE 2023 · Region 2 · Set 1 · Q31 · 5 marks
(i)Use Gauss' law to obtain an expression for the electric field due to an infinitely long thin straight wire with uniform linear charge density $\displaystyle \lambda$.(ii)An infinitely long positively charged straight wire has a linear charge density $\displaystyle \lambda$. An electron is revolving in a circle with a constant speed $\displaystyle v$ such that the wire passes through the centre, and is perpendicular to the plane, of the circle. Find the kinetic energy of the electron in terms of magnitudes of its charge and linear charge density $\displaystyle \lambda$ on the wire.(iii)Draw a graph of kinetic energy as a function of linear charge density $\displaystyle \lambda$.(i)Consider two identical point charges located at points $\displaystyle ( 0,0 )$ and (a, $\displaystyle 0$).(1)Is there a point on the line joining them at which the electric field is zero ?(2)Is there a point on the line joining them at which the electric potential is zero? Justify your answers for each case.(ii)State the significance of negative value of electrostatic potential energy of a system of charges. Three charges are placed at the corners of an equilateral triangle ABC of side $\displaystyle 2.0$ m as shown in figure. Calculate the electric potential energy of the system of three charges. 
(i)
Use Gauss' law to obtain an expression for the electric field due to an infinitely long thin straight wire with uniform linear charge density $\displaystyle \lambda$.
(ii)
An infinitely long positively charged straight wire has a linear charge density $\displaystyle \lambda$. An electron is revolving in a circle with a constant speed $\displaystyle v$ such that the wire passes through the centre, and is perpendicular to the plane, of the circle. Find the kinetic energy of the electron in terms of magnitudes of its charge and linear charge density $\displaystyle \lambda$ on the wire.
(iii)
Draw a graph of kinetic energy as a function of linear charge density $\displaystyle \lambda$.
(i)
Consider two identical point charges located at points $\displaystyle ( 0,0 )$ and (a, $\displaystyle 0$).
(1)
Is there a point on the line joining them at which the electric field is zero ?
(2)
Is there a point on the line joining them at which the electric potential is zero? Justify your answers for each case.
(ii)
State the significance of negative value of electrostatic potential energy of a system of charges. Three charges are placed at the corners of an equilateral triangle ABC of side $\displaystyle 2.0$ m as shown in figure. Calculate the electric potential energy of the system of three charges.
Marking-scheme solution
Electric Charges and FieldsApplications of Gauss’s LawApplylong_answerhard
More from Electric Charges and Fields
- (i) Two point charges +q and -q are held at (a, 0) and ( -a, 0 ) in x-y plane. Obtain an expression for the…2025 · asked 3×
- An electric dipole consists of two point charges q and -q separated by a distance 2a. Derive an expression…2026 · asked 3×
- (i) Define electric flux and write its SI unit. (ii) Use Gauss' law to obtain the expression for the electric…2023 · asked 3×
- Two small solid metal balls A and B of radii R and 2 R having charge densities 2 σ and 3 σ respectively are…2025 · asked 3×
- (i) The electric field in a region is given by E=40 x i N / C. Find the amount of work done in taking a unit…2025 · asked 3×
- Four point charges of 1 μ C,-2 μ C, 1 μ C and -2 μ C are placed at the corners A, B, C and D respectively, of…2024 · asked 3×
- Which one of the following statements is correct? Electric field due to static charges is2025 · asked 3×
- A point charge situated at a distance ' r ' from a short electric dipole on its axis, experiences a force F.…2023 · asked 3×
CBSE Class 12 Physics past-paper question from the 2023board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.