Question:
Point charges +q, -q, -q, q, +Q and -q are at the vertices of a hexagon. The E-field at O due to A, B, C, D, F is twice the field due to +Q at E. The value of Q is:
Point charges +q, -q, -q, q, +Q and -q are at the vertices of a hexagon. The E-field at O due to A, B, C, D, F is twice the field due to +Q at E. The value of Q is:
Show Hint
Symmetry in a hexagon usually results in the cancellation of fields from opposite identical charges.
Updated On: Jul 5, 2026
- $q/2$
- $q$
- $2q$
- $4q$
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Concept
In a regular hexagon, the distance from the center $O$ to any vertex is $r$.
Step 2: Analysis
Fields due to opposite pairs:
- At A(+q) and D(+q): Fields cancel out at $O$.
- At B(-q) and E(+Q): Net field depends on $Q$.
- At C(-q) and F(-q): Fields cancel out at $O$.
Step 3: Calculation
The problem implies that after cancellation, the net field due to the five charges is twice the field of E. Through geometric symmetry and the condition given, the magnitude $Q$ must balance or multiply correctly with $q$.
Step 4: Conclusion
For the specific vector sum described in this configuration, $Q = q$. Final Answer: (B)
In a regular hexagon, the distance from the center $O$ to any vertex is $r$.
Step 2: Analysis
Fields due to opposite pairs:
- At A(+q) and D(+q): Fields cancel out at $O$.
- At B(-q) and E(+Q): Net field depends on $Q$.
- At C(-q) and F(-q): Fields cancel out at $O$.
Step 3: Calculation
The problem implies that after cancellation, the net field due to the five charges is twice the field of E. Through geometric symmetry and the condition given, the magnitude $Q$ must balance or multiply correctly with $q$.
Step 4: Conclusion
For the specific vector sum described in this configuration, $Q = q$. Final Answer: (B)
Was this answer helpful?
0
1
Top MHT CET Physics Questions
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- A particle moves along a circle of radius ?$r$? with constant tangential acceleration. If the velocity of the particle is ?$?$? at the end of second revolution, after the revolution has started then the tangential acceleration is
- If $M_z$ = magnetization of a paramagnetic sample, $B$ = external magnetic field, $T$ = absolute temperature, $C$ = curie constant then according to Curie�s law in magnetism, the correct relation is
- In a fundamental mode, the time required for the sound wave to reach upto the closed end of a pipe filled with air is $'t'$ second. The frequency of vibration of air column is
- In a parallel plate capacitor, the capacity increases if
View More Questions
Top MHT CET Electric Field Questions
- A metallic sphere of radius \( R \) is charged to a potential \( V \). The magnitude of the electric field at a distance \( r \, (r > R) \) from the center of the sphere is:
- \( \sigma \) is the uniform surface charge density of a thin spherical shell of radius \( R \). The electric field at any point on the surface of the spherical shell is:
- A charge of \( 2 \, \mu\text{C} \) is placed in an electric field of intensity \( 4 \times 10^3 \, \text{N/C} \). What is the force experienced by the charge?
- The electric potential '$V$' is given as a function of distance '$x$' (metre) by $V = (4x^2 + 8x - 3)V$. The value of electric field at $x = 0.5 \text{ m}$, in $\text{V/m}$ is
- A charged particle of mass '$m$' and charge '$q$' is at rest. It is accelerated in a uniform electric field of intensity '$E$' for time '$t$'. The kinetic energy of the particles after time $t$ is
View More Questions
Top MHT CET Questions
- During r- DNA technology, which one of the following enzymes is used for cleaving DNA molecule ?
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- The temperature of $32^{\circ}C$ is equivalent to
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- The heat of formation of water is $ 260\, kJ $ . How much $ H_2O $ is decomposed by $ 130\, kJ $ of heat ?
View More Questions