{
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   "source": [
    "# Chapter 2 Electrostatics "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 2_1 pgno:13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Resultant force acting on charge at C= N 12.72\n"
     ]
    }
   ],
   "source": [
    "from math import pi,sqrt,cos,sin\n",
    "\n",
    "epsilon=8.854e-12\n",
    "r=sqrt(.1**2+.1**2)#distance b/w A and C\n",
    "Fca=(2e-6)*(4e-6)/(4*pi*epsilon*r**2)#from A to C\n",
    "Fcb=(4e-6)*(2e-6)/(4*pi*epsilon*.1**2)#from C to B\n",
    "Fcd=(4e-6)*(4e-6)/(4*pi*epsilon*.1**2)#from C to D\n",
    "#Fr has horizontal and vertical components as Frx and Fry respectively\n",
    "Frx=Fcd-Fca*cos(45*pi/180)\n",
    "Fry=Fcb-Fca*sin(45*pi/180)\n",
    "Fr=sqrt(Frx**2+Fry**2)\n",
    "print\"Resultant force acting on charge at C= N\", round(Fr,2)\n",
    "#error in textbook answer\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 2_ pgno:15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Resultant intensity on charge at C=*10**4 N/C at angle  eegrees 25.44 37.0\n"
     ]
    }
   ],
   "source": [
    "from math import pi,cos,sin,sqrt,atan\n",
    "epsilon=8.854e-12\n",
    "E1=(4e-8)/(4*pi*epsilon*.05**2)#fiele intensity eue to charge at A,eirection is from e to A\n",
    "r=sqrt(2*.05**2)#eistance b/w B ane e\n",
    "E2=(4e-8)/(4*pi*epsilon*r**2)#fiele intensity eue to charge at B,eirection is from B to e along eiagonal Be\n",
    "E3=(8e-8)/(4*pi*epsilon*.05**2)#fiele intensity eue to charge at C,eirection is from e to C\n",
    "#Er has horizontal ane vertical components as Erx ane Ery respectively\n",
    "Erx=E3-E2*cos(45*pi/180)\n",
    "Ery=-E1+E2*sin(45*pi/180)\n",
    "Er=sqrt(Erx**2+Ery**2)\n",
    "theta=atan(Ery/Erx)\n",
    "print\"Resultant intensity on charge at C=*10**4 N/C at angle  eegrees\", round(Er/10**4,2),round(-theta*100)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 2_3 pgno:15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Potential at A eue to charges at B, C ane e= V 3.73\n"
     ]
    }
   ],
   "source": [
    "from math import pi,sqrt\n",
    "epsilon=8.854e-12\n",
    "AB=.05\n",
    "BC=.07\n",
    "AC=sqrt(.05**2+.07**2)\n",
    "V1=2e-10/(4*pi*epsilon*.05)#potential at A eue to charge at B\n",
    "V2=-8e-10/(4*pi*epsilon*AC)#potential at A eue to charge at C\n",
    "V3=4e-10/(4*pi*epsilon*.07)#potential at A eue to charge at e\n",
    "V=V1+V2+V3 \n",
    "print\"Potential at A eue to charges at B, C ane e= V\", round(V,2)\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 2_4 pgno:16"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time constant T= sec\n",
      "0.015\n",
      "Initial current= A\n",
      "0.2\n",
      "Charge on the capacitor after 0.05 sec is  C\n",
      "0.003\n",
      "Charging current after 0.05 sec is  A\n",
      "0.007\n",
      "Charging current after 0.015 sec is  A\n",
      "0.074\n",
      "Voltage across 500 ohm resistor after 0.05 sec is  V 3.567\n"
     ]
    }
   ],
   "source": [
    "from math import exp\n",
    "C=30e-6\n",
    "R=500.\n",
    "T=C*R\n",
    "print\"Time constant T= sec\\n\", round(T,3)\n",
    "#at t=0sec, voltage across capacitor is zero\n",
    "V=100.#apliee voltage\n",
    "I=V/R#Ohm's Law\n",
    "print\"Initial current= A\\n\", round(I,3)\n",
    "t=.05\n",
    "Q=C*V\n",
    "q=Q*(1-exp(-t/T))\n",
    "print\"Charge on the capacitor after 0.05 sec is  C\\n\", round(q,3)\n",
    "i1=I*exp(-t/T)\n",
    "print\"Charging current after 0.05 sec is  A\\n\",round(i1,3)\n",
    "t=.015\n",
    "i2=I*exp(-t/T)\n",
    "print\"Charging current after 0.015 sec is  A\\n\",round(i2,3)\n",
    "V=i1*R\n",
    "print\"Voltage across 500 ohm resistor after 0.05 sec is  V\", round(V,3)\n",
    "#answers vary from the textbook eue to roune off error\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 2_5 pgno:17"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P.e. across the combination = V\n",
      "133.33\n",
      "Electrostatic energy before capacitors are connectee in parallel= J\n",
      "2.0\n",
      "Electrostatic energy after capacitors are connectee in parallel= J 1.33\n"
     ]
    }
   ],
   "source": [
    "\n",
    "C=100e-6\n",
    "V=200\n",
    "Q=C*V\n",
    "Ct=100e-6+50e-6#total capacitance\n",
    "Vt=Q/Ct\n",
    "print\"P.e. across the combination = V\\n\", round(Vt,2)\n",
    "EE1=100e-6*V**2/2\n",
    "print\"Electrostatic energy before capacitors are connectee in parallel= J\\n\", EE1\n",
    "EE2=Ct*Vt**2/2\n",
    "print\"Electrostatic energy after capacitors are connectee in parallel= J\",round( EE2,2)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 2_6 pgno:18"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Three capacitors have capacitances  microF,  microF ane  microF\n",
      "80.0 100.0 120.0\n",
      "Voltage across the combination = V 50.0\n"
     ]
    }
   ],
   "source": [
    "\n",
    "C1=100e-6  #capacitance of first capacitor which is to be chargee\n",
    "V=200.  #voltage across C1\n",
    "Q=C1*V\n",
    "#Let Q1, Q2, Q3, Q4 be the charges on respective capacitors after connection\n",
    "Q2=4000e-6\n",
    "Q3=5000e-6\n",
    "Q4=6000e-6\n",
    "Q1=Q-(Q2+Q3+Q4)\n",
    "C2=C1*(Q2/Q1)\n",
    "C3=C1*(Q3/Q1)\n",
    "C4=C1*(Q4/Q1)\n",
    "print\"Three capacitors have capacitances  microF,  microF ane  microF\\n\", C2*10**6,C3*10**6,C4*10**6\n",
    "Vt=Q1/C1\n",
    "print\"Voltage across the combination = V\", Vt\n"
   ]
  }
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