## Electric Field due to N Point Charges Solution

STEP 0: Pre-Calculation Summary
Formula Used
Electric Field due to N Point Charges = sum(x,1,Number of Point Charges,(Charge)/(4*pi*[Permitivity-vacuum]*(Distance from Electric Field-Charge Distance)^2))
Er = sum(x,1,n,(q)/(4*pi*[Permitivity-vacuum]*(R-Rm)^2))
This formula uses 2 Constants, 1 Functions, 5 Variables
Constants Used
[Permitivity-vacuum] - Permittivity of vacuum Value Taken As 8.85E-12
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
sum - Summation or sigma (∑) notation is a method used to write out a long sum in a concise way., sum(i, from, to, expr)
Variables Used
Electric Field due to N Point Charges - (Measured in Volt per Meter) - Electric Field due to N Point Charges is the vector sum of the electric fields produced by each of the N point charges, considering their magnitudes, distances, and the medium's permittivity.
Number of Point Charges - Number of Point Charges is the number of total point charges which are responsible for the generation of electric field at point P.
Charge - (Measured in Coulomb) - A Charge is the fundamental property of forms of matter that exhibit electrostatic attraction or repulsion in the presence of other matter.
Distance from Electric Field - (Measured in Meter) - Distance from Electric Field represents the distance from origin to point P where electric filed is to be calculated.
Charge Distance - (Measured in Meter) - Charge Distance denotes the distance of point charge from origin which generates the electric field at point P.
STEP 1: Convert Input(s) to Base Unit
Number of Point Charges: 7 --> No Conversion Required
Charge: 0.3 Coulomb --> 0.3 Coulomb No Conversion Required
Distance from Electric Field: 4.997 Meter --> 4.997 Meter No Conversion Required
Charge Distance: 3.889 Meter --> 3.889 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Er = sum(x,1,n,(q)/(4*pi*[Permitivity-vacuum]*(R-Rm)^2)) --> sum(x,1,7,(0.3)/(4*pi*[Permitivity-vacuum]*(4.997-3.889)^2))
Evaluating ... ...
Er = 15381073207.6207
STEP 3: Convert Result to Output's Unit
15381073207.6207 Volt per Meter --> No Conversion Required
15381073207.6207 1.5E+10 Volt per Meter <-- Electric Field due to N Point Charges
(Calculation completed in 00.006 seconds)
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Created by Vignesh Naidu
Vellore Institute of Technology (VIT), Vellore,Tamil Nadu
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## < 17 Electromagnetic Radiation and Antennas Calculators

Average Power Density of Half-Wave Dipole
Average Power Density = (0.609*Intrinsic Impedance of Medium*Amplitude of Oscillating Current^2)/(4*pi^2*Radial Distance From Antenna^2)*sin((((Angular Frequency of Half Wave Dipole*Time)-(pi/Length of Antenna)*Radial Distance From Antenna))*pi/180)^2
Magnetic Field for Hertzian Dipole
Magnetic Field Component = (1/Dipole Distance)^2*(cos(2*pi*Dipole Distance/Wavelength of Dipole)+2*pi*Dipole Distance/Wavelength of Dipole*sin(2*pi*Dipole Distance/Wavelength of Dipole))
Maximum Power Density of Half-Wave Dipole
Maximum Power Density = (Intrinsic Impedance of Medium*Amplitude of Oscillating Current^2)/(4*pi^2*Radial Distance From Antenna^2)*sin((((Angular Frequency of Half Wave Dipole*Time)-(pi/Length of Antenna)*Radial Distance From Antenna))*pi/180)^2
Power Radiated by Half-wave Dipole = ((0.609*Intrinsic Impedance of Medium*(Amplitude of Oscillating Current)^2)/pi)*sin(((Angular Frequency of Half Wave Dipole*Time)-((pi/Length of Antenna)*Radial Distance From Antenna))*pi/180)^2
Power that Crosses Surface of Sphere
Power Crossed at Sphere Surface = pi*((Amplitude of Oscillating Current*Wavenumber*Short Antenna Length)/(4*pi))^2*Intrinsic Impedance of Medium*(int(sin(Theta)^3*x,x,0,pi))
Electric Field due to N Point Charges
Electric Field due to N Point Charges = sum(x,1,Number of Point Charges,(Charge)/(4*pi*[Permitivity-vacuum]*(Distance from Electric Field-Charge Distance)^2))
Poynting Vector Magnitude
Poynting Vector = 1/2*((Dipole Current*Wavenumber*Source Distance)/(4*pi))^2*Intrinsic Impedance*(sin(Polar Angle))^2
Total Radiated Power in Free Space
Total Radiated Power in Free Space = 30*Amplitude of Oscillating Current^2*int((Dipole Antenna Pattern Function)^2*sin(Theta)*x,x,0,pi)
Radiation Resistance = 60*(int((Dipole Antenna Pattern Function)^2*sin(Theta)*x,x,0,pi))
Time Average Radiated Power of Half-Wave Dipole
Time Average Radiated Power = (((Amplitude of Oscillating Current)^2)/2)*((0.609*Intrinsic Impedance of Medium)/pi)
Polarization
Polarization = Electric Susceptibility*[Permitivity-vacuum]*Electric Field Strength
Radiation Resistance of Half-wave Dipole = (0.609*Intrinsic Impedance of Medium)/pi
Directivity of Half-Wave Dipole
Directivity of Half Wave Dipole = Maximum Power Density/Average Power Density
Electric Field for Hertzian Dipole
Electric Field Component = Intrinsic Impedance*Magnetic Field Component
Radiation Efficiency of Antenna = Maximum Gain/Maximum Directivity
Average Power
Average Power = 1/2*Sinusoidal Current^2*Radiation Resistance
Radiation Resistance = 2*Average Power/Sinusoidal Current^2

## Electric Field due to N Point Charges Formula

Electric Field due to N Point Charges = sum(x,1,Number of Point Charges,(Charge)/(4*pi*[Permitivity-vacuum]*(Distance from Electric Field-Charge Distance)^2))
Er = sum(x,1,n,(q)/(4*pi*[Permitivity-vacuum]*(R-Rm)^2))

## What are the Applications of Electric Field due to N Point Charges ?

1. Electron Microscopy: By analyzing the electric field generated by a focused electron beam interacting with a sample, electron microscopes achieve high-resolution magnified images for studying materials at the atomic level.

2. Ion implantation: This technique utilizes an electric field to accelerate ions towards a target material, implanting them for doping purposes in semiconductor devices or modifying material properties.

3. Electrostatic Precipitators: These air pollution control devices use strong electric fields to attract and remove dust particles and other pollutants from industrial exhaust gases.

## How to Calculate Electric Field due to N Point Charges?

Electric Field due to N Point Charges calculator uses Electric Field due to N Point Charges = sum(x,1,Number of Point Charges,(Charge)/(4*pi*[Permitivity-vacuum]*(Distance from Electric Field-Charge Distance)^2)) to calculate the Electric Field due to N Point Charges, The Electric Field due to N Point Charges formula is defined as the vector sum of the electric fields produced by each of the N point charges, considering their magnitudes, distances, and the medium's permittivity. Electric Field due to N Point Charges is denoted by Er symbol.

How to calculate Electric Field due to N Point Charges using this online calculator? To use this online calculator for Electric Field due to N Point Charges, enter Number of Point Charges (n), Charge (q), Distance from Electric Field (R) & Charge Distance (Rm) and hit the calculate button. Here is how the Electric Field due to N Point Charges calculation can be explained with given input values -> 1.5E+10 = sum(x,1,7,(0.3)/(4*pi*[Permitivity-vacuum]*(4.997-3.889)^2)).

### FAQ

What is Electric Field due to N Point Charges?
The Electric Field due to N Point Charges formula is defined as the vector sum of the electric fields produced by each of the N point charges, considering their magnitudes, distances, and the medium's permittivity and is represented as Er = sum(x,1,n,(q)/(4*pi*[Permitivity-vacuum]*(R-Rm)^2)) or Electric Field due to N Point Charges = sum(x,1,Number of Point Charges,(Charge)/(4*pi*[Permitivity-vacuum]*(Distance from Electric Field-Charge Distance)^2)). Number of Point Charges is the number of total point charges which are responsible for the generation of electric field at point P, A Charge is the fundamental property of forms of matter that exhibit electrostatic attraction or repulsion in the presence of other matter, Distance from Electric Field represents the distance from origin to point P where electric filed is to be calculated & Charge Distance denotes the distance of point charge from origin which generates the electric field at point P.
How to calculate Electric Field due to N Point Charges?
The Electric Field due to N Point Charges formula is defined as the vector sum of the electric fields produced by each of the N point charges, considering their magnitudes, distances, and the medium's permittivity is calculated using Electric Field due to N Point Charges = sum(x,1,Number of Point Charges,(Charge)/(4*pi*[Permitivity-vacuum]*(Distance from Electric Field-Charge Distance)^2)). To calculate Electric Field due to N Point Charges, you need Number of Point Charges (n), Charge (q), Distance from Electric Field (R) & Charge Distance (Rm). With our tool, you need to enter the respective value for Number of Point Charges, Charge, Distance from Electric Field & Charge Distance and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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