Tuesday, April 7, 2015

HP Prime: Electric Field & Flux (Gauss’s Law)

HP Prime:  Electric Field & Flux (Gauss’s Law)

The program EFILED calculates the electric filed and flux for five common fields:

Ring

Line or Wire of Charge  The radius of the Wire is small.

Sphere (non-conducting – uniform charge)

Plane (Flat Sheet)

Cylinder with the charge flowing through the ends

By Gauss’s Law, the general formula that of flux is:

Flux =  q/ε0 = ∫ E dA

Where:
q = charge (in Coulombs)
ε0 = 8.85418781762 * 10^-12 F/m
E = electric field
dA = change of area, where A represents Area

HP Prime: EFIELD

EXPORT EFIELD()
BEGIN
// Electric Filed & Flux
// EWS 2015-04-07
// SI Units ares assumed
// ε0=8.85418781762ᴇ−12_(F/m)

LOCAL c,ef,sa,flux;
// ef: electric field
// sa: surface area
// flux = ef * sa = q/ε

CHOOSE(c,"Elec. Field/Flux",
{"Ring","Line/Wire of Charge",
"Non-Conducting Sphere",
"Plane","Cylinder"});

IF c==0 THEN KILL; END;

// Ring
IF c==1 THEN
LOCAL ro,ri,a,q;
INPUT({ro,ri,a,q},"Elec. Filed: Ring",
{"ro=","ri=","a=","q="},
"Point","Charge"});
ef:=q/(4*8.85418781762ᴇ−12*π*
((ro-ri)^2+a^2)^1.5);
sa:=π*(ro^2-ri^2);
END;

// Line/Wire of Charge
IF c==2 THEN
LOCAL l,r,a,y,q;
INPUT({l,r,a,q},"Elec. Field: Line",
{"l =","r =","a =","q ="},{"Length of Wire",
"Radius of Wire","Distance from Wire",
"Charge"});
ef:=(q*a)/(l*4*8.85418781762ᴇ−12*π)
*∫((y^2+a^2)^−1.5,y,−l/2,l/2);
sa:=π*l*2*π;
END;

// Non-Conducting Sphere
IF c==3 THEN
LOCAL R,r,q,p;
INPUT({R,r,q},"Non-Conducting Sphere",
{"R =","r =","q ="},{"Radius of Sphere",
IF r<R THEN
sa:=4*π*r^2;
p:=q/(4/3*π*r^3);
ef:=(p*r)/(3*8.85418781762ᴇ−12);
ELSE
sa:=4*π*R^2;
p:=q/(4/3*π*R^3);
ef:=(p*R^3)/(3*8.85418781762ᴇ−12*r^2);
END;
END;

// Plane
IF c==4 THEN
LOCAL A,q;
INPUT({A,q},"Elec. Field: Plane",
{"A =","q ="},{"Sheet Area","Charge"});
ef:=q/(2*8.85418781762ᴇ−12*A);
sa:=A;
END;

// Cylinder
IF c==5 THEN
LOCAL R,r,L,q,p;
INPUT({R,r,L,q},"Non-Conducting Sphere",
{"R =","r =","L =","q ="},{
"Length of Cylinder",
"Charge"});
IF r<R THEN
sa:=2*π*r*L;
p:=q/(π*r^2*L);
ef:=(p*r)/(2*8.85418781762ᴇ−12);
ELSE
sa:=2*π*R*L;
p:=q/(π*R^2);
ef:=(p*R^2)/(2*8.85418781762ᴇ−12*r);
END;
END;

flux:=ef*sa;
PRINT();
PRINT("Electric Field: "+ef);
PRINT("Electric Flux: "+flux);
RETURN({ef, flux});

END;

Eddie

This blog is property of Edward Shore.  2015

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