Four charges Q1 , Q2 , Q3 and Q4 are placed on the four corners of a square of side 1m. Calculate the potential at the centre of the square. The values of the charges are given as Q1 = 1.0 × 10^−9 C, Q2 = 2 × 10^−9 C, Q3 = 3 × 10^−9 C and Q4 = 4 × 10^−9 C. The charges are placed in air.

Question

Four charges [latex]Q_{1} , Q_{2} , Q_{3}[/latex] and [latex] Q_{4}[/latex] are placed on the four corners of a square of side 1m. Calculate the potential at the centre of the square. The values of the charges are given as [latex]Q_{1} = 1.0 × 10^{−9} C, Q_{2} = 2 × 10^{−9} C, Q_{3} = 3 × 10^{−9} C [/latex] and [latex]Q_{4} = 4 × 10^{−9} C[/latex] . The charges are placed in air.

Accepted Answer

Distance BD =[latex]\sqrt{1^{2}+1^{2}} =\sqrt{2}[/latex]

Distance BX =[latex]\frac{\sqrt{2}}{2}=\frac{1}{\sqrt{2}}[/latex] m

The potential at point X is due to the combined effect of the four charges. The potential at X, i.e. [latex]V_{X}[/latex] is

[latex]V_{x}=\frac{q_{1}}{4\pi \varepsilon _{0}r_{1}}+\frac{q_{2}}{4\pi \varepsilon _{0}r_{2}}+\frac{q_{3}}{4\pi \varepsilon _{0}r_{3}}+\frac{q_{4}}{4\pi \varepsilon _{0}r_{4}}[/latex]

Since [latex]r_{1} = r_{2} = r_{3} = r_{4} , r = [/latex] Distance BX [latex]=\frac{1}{\sqrt{2} } [/latex] m.

[latex]V_{X}=\frac{1}{4\pi \varepsilon _{0}r} ( q_{1}+ q_{2} + q_{3} + q_{4} )[/latex]

[latex]=9 imes 10^{9} imes \sqrt{2}(1 imes 10^{-9}+2 imes 10^{-9}+3 imes 10^{-9}+4 imes 10^{-9})[/latex]

[latex]=9 imes 10^{9} imes \sqrt{2} imes 10^{-9} imes 10[/latex]

= 90 × 1.414
= 127.26 volts

Question 1.2: Four charges Q1 , Q2 , Q3 and Q4 are placed on the four corn...

Related Answered Questions

Calculate the energy stored in a parallel plate capacitor, which consists of two metal plates of 64 cm² separated by a dielectric 1 mm thick with µr= 4.0. A potential difference of 1 kV is applied across it. What amount of heat will be produced when the charged capacitor is ...

Verified Answer:

Calculate the electric field strength at a distance of 50 cm from a point charge of 1 × 10^−6 coulomb placed in air. ...

Verified Answer:

Two point charges Q1= + 2× 10^−8 C and Q2 = −3× 10^−8 C are separated from each other by 2 m. Determine the electric field at the mid- point between the two charges. ...

Verified Answer:

Two positive charges of magnitude 1 × 10^−6 coulomb are placed in air at a distance of 2 m from each other. Calculate the potential at a point P which is 1 m above the middle of the distance between the charges. ...

Verified Answer:

Three point charges of magnitude Q = 1 × 10^−6 coulombs are located in the three corners of an equilateral triangle of side 1 m. Find the force on one charge due to the other two charges. ...

Verified Answer:

A co-axial cable with a central core of 2 mm diameter passes through the centre of a cylinder made of dielectric material diameter 5 mm. The dielectric cylinder is coated from outside with a conducting sheath. The outer conducting sheath is at ground potential. Calculate the capacitance of the ...

Verified Answer:

Two point charges of 2 microfarad and −4 µF each are placed at a distance of 1m from each other on a straight line. Determine at what point the potential will be zero. ...

Verified Answer:

A ring of inner diameter R and outer diameter R + 2 in the x−y plane with z = 0, has uniform surface charge density ρs . Calculate the potential at the centre of the ring. ...

Verified Answer:

Three charges of 5 × 10^−9 C each are placed on the three corners of a rectangle ABCD. Calculate the potential at the fourth corner point of the rectangle. The sides of the rectangle are given as AB = CD = 4 m and BC = DA = 3 m. The medium is air. ...

Verified Answer:

Three charges of 3 × 10^−9 C each are placed in the three corners of an equilateral triangle of side 3 m. Calculate the potential at the centroid of the triangle. ...

Verified Answer: