Chapter 21 potential 第八章静电场 Chapter 21 Electric potential 1. Electric potential and potential difference 2. Relation between electric potential and Electric field 3. The calculation of electric potential 4. Equipotential Surfaces 5. Electrostatic Potential Energy
Chapter 21 potential 第八章静电场 1. Electric Potential and Potential Difference 2. Relation Between Electric Potential and Electric Field 3. The Calculation of Electric Potential 4. Equipotential Surfaces 5. Electrostatic Potential Energy
Chapter 21 potential 第八章静电场 New words and Expressions electric potential 电势 potential difference 电势差,电压 circulation theorem 环路定理 electric potential energy 电势能 equipotential surfaces 等势面 electric potential gradient 电势梯度
Chapter 21 potential 第八章静电场 New words and Expressions electric potential 电势 potential difference 电势差,电压 circulation theorem 环路定理 electric potential energy 电势能 equipotential surfaces 等势面 electric potential gradient 电势梯度
Chapter 21 potential 第八章静电场 21-1&21-8 Electric Potential and Potential Difference(p503-505, p515) To study the electric field from the w, we introduce v(electric potential). 1. Features of electrostatic force Coulomb's aw for 1 g,g F electrostatic force 2 Newton 's law for nmin gravitational force: F=G Mathematically identical! Many properties for the gravitational may also be true for electrostatic forces
Chapter 21 potential 第八章静电场 To study the electric field from the W, we introduce V (electric potential). 21-1&21-8 Electric Potential and Potential Difference (p503-505, p515) 1. Features of Electrostatic Force Coulomb’s Law for electrostatic force: 2 1 2 4 0 1 r q q F Newton’s Law for gravitational force: 2 1 2 r m m F G Mathematically identical! Many properties for the gravitational may also be true for electrostatic forces
Chapter 21 potential 第八章静电场 1)Work done by electrostatic Force 点电荷的电场 Electric field of a point charge dW=anE·da B ggo 4兀F,d7 B F·dl= rdl cos e=rdr q40 0 4π60
Chapter 21 potential 第八章静电场 q 1) Work done by Electrostatic Force 0 q r W q E l d d 0 r l r qq d 4π 3 0 0 r dl rdl cos rdr r r qq W d 4π d 2 0 0 点电荷的电场 Electric field of a point charge l d dr Ar A Br B E
Chapter 21 potential 第八章静电场 w= go r's dr B 4兀E0nr dr入O ggo B 4πE0 结果:W仅与q的始末 位置有关,与路径无关 0 任意电荷的电场(视为点电荷的组合) E=∑E,W=qE=∑ q,E2·dl
Chapter 21 potential 第八章静电场 B A r r r qq r W 2 0 0 d 4π 0 q r l d dr Ar A Br B E ) 1 1 ( 4π 0 0 A B r r qq 结果: 仅与 的始末 位置有关，与路径无关. 0 W q 任意电荷的电场（视为点电荷的组合） i E Ei l W q E l 0 d l i i q E l 0 d
Chapter 21 potential 第八章静电场 结论:静电场力做功与路径无关. The work done by electrostatic force is path independent The electrostatic force is a conservative force. 静电场是保守场
Chapter 21 potential 第八章静电场 The work done by electrostatic force is path independent. The electrostatic force is a conservative force. 结论：静电场力做功与路径无关. 静电场是保守场
Chapter 21 potential 第八章静电场 2) Circulation theorem:静电场的环路定理 在静电场中,电场强度沿闭合路径的线积分等于零。或 电场力移动单位电荷沿闭合路径一周所做的功为0。 The line integral of the electrostatic field around a closed loop is zero qE·d=qo「E·dl B AlB A2 B q(∫Ed+∫E·d)=0 2 alB B2A Edl=o
Chapter 21 potential 第八章静电场 2) Circulation theorem: 静电场的环路定理 0。 The line integral of the electrostatic field around a closed loop is zero. E A B A B q E l q E l 2 0 1 0 d d ( d d ) 0 1 2 0 A B B A q E l E l d 0 l E l 1 2 A B
Chapter 21 potential 第八章静电场 2. Electric Potential Energy电势能(PS15): Because electrostatic force is a conservative force an electric potential energy U can be introduced: 静电场是保守场,静电场力是保守力静电场力 所做的功就等于电荷电势能增量的负值. A→B AB.edI 如B (UR-U △U
Chapter 21 potential 第八章静电场 Because electrostatic force is a conservative force, an electric potential energy U can be introduced: 2. Electric Potential Energy 电势能(P515): 静电场是保守场，静电场力是保守力.静电场力 所做的功就等于电荷电势能增量的负值. U U U W q E l B A AB A B ( ) d 0 E 0 q A B
Chapter 21 potential 第八章静电场 To ensure U at a point, a reference potential energy should be chosen B=0,U 0 The U of charge g at arbitrary B point a= the work done by the fe during the move or/4g E charge g from a to infinity 试验电荷Q。在电场中某点的电势能,在数值上 就等于把它从该点移到零势能处静电场力所作的功 电势能的大小是相对的,电势能的差是绝对的
Chapter 21 potential 第八章静电场 To ensure U at a point, a reference potential energy should be chosen: 0, UB The U of charge q at arbitrary point a = the work done by the during the move of charge q from a to infinity. Fe AB A U q E l 0 d 试验电荷 在电场中某点的电势能，在数值上 就等于把它从该点移到零势能处静电场力所作的功. q0 电势能的大小是相对的，电势能的差是绝对的. E 0 q A B
Chapter 21 potential 第八章静电场 3. Electric Potential(P503): The physical quantity to represent property of field at any point - electric potential. A Electric potential at point a is the potential energy per unit charge. =0点 A E·dl A
Chapter 21 potential 第八章静电场 The physical quantity to represent property of field at any point —— electric potential. 3. Electric Potential (P503): q U V A A Electric potential at point a is the potential energy per unit charge. V E l V A A d 0 点 AB A U q E l 0 d