Q17.The electric potential V (x) in a region around the origin is given by V (x) = 4x2 volts. The electric charge enclosed in a cube of 1 m side with its centre at the origin is (in coulomb) (1) 8ε0 (2) −4ε0 (3) 0 (4) −8ε0 JEE Main 2012 (07 May Online) JEE Main Previous Year Paper
What This Question Tests
The question requires deriving the electric field from the potential and then using Gauss's law in differential form to determine the charge density and subsequently the enclosed charge.
Concepts Tested
Formulas Used
E = -∇V
∇⋅E = ρ/ε₀
Q_enc = ∫ρ dV
📚 NCERT Sections This Tests
1.18 — A Point Charge Of 2.0 Mc Is At The Centre Of A Cubic Gaussian
Physics Class 11 · Chapter 1
1.18 A point charge of 2.0 mC is at the centre of a cubic Gaussian surface 9.0 cm on edge. What is the net electric flux through the surface?
2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
Physics Class 11 · Chapter 2
2.1 Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
1.17 — A Point Charge +10 Mc Is A Distance 5 Cm Directly Above The Centre
Physics Class 11 · Chapter 1
1.17 A point charge +10 mC is a distance 5 cm directly above the centre of a square of side 10 cm, as shown in Fig. 1.31. What is the magnitude of the electric flux through the square? (Hint: Think of the square as one face of a cube with edge 10 cm.) FIGURE 1.31
📋 Question Details
- Chapter
- Electrostatics
- Topic
- Electric potential, electric field, Gauss's Law
- Year
- 2012
- Shift
- 07 May Online
- Q Number
- Q17
- Type
- MCQ
- NCERT Ref
- Class 12 Physics Ch 1: Electric Charges and Fields
More from this Chapter
Q43.A charged particle q is placed at the centre O of cube of length L (A B C D E F G H). Another same charge q is placed at a distance L from O. Then the electric flux through ABCD is (1) q/4πϵ0L (2) zero (3) q/2πϵ0L (4) q/3πϵ0L
Q44.If a charge q is placed at the centre of the line joining two equal charges Q such that the system is in equilibrium then the value of q is (1) Q/2 (2) −Q/2 (3) Q/4 (4) −Q/4
Q45.If there are n capacitors in parallel connected to V volt source, then the energy stored is equal to (1) CV (2) 12 nCV2 (3) CV2 (4) 2n1 CV 2
Q46.Capacitance (in F ) of a spherical conductor with radius 1 m is (1) 1.1 × 10−10 (2) 10−6 (3) 9 × 10−9 (4) 10−3