1.1.5. Coulomb law in reality the principle of superposition The concept of density of charge: line density 2(r), surface density o(r) and volume density p(r") Point to line F ea ri(r 4丌 F=9 Point to surface a P(7) Point to volume 4兀S Line to line F A()(r) Br-r)dld - Surface to surface F o(ro(r 4T 8 r-r P(rp(r Volume to volume r-r)dsds 4兀S
1.1.5. Coulomb law in reality & the principle of superposition Point to line: Point to surface Point to volume Line to line Surface to surface Volume to volume The concept of density of charge : line density , surface density (r ) and volume density . (r ) (r ) ds Q r F r r o o s a 2 ( ) 4 = dv Q r F r r o o v a 2 ( ) 4 = r dl r Q r F l a 0 2 0 ( ) 4 = ' ( ) ( ) 4 1 3 ( ) ' dsds r r F r r o s s r r − − = ' ( ) ( ) 4 1 3 ( ) ' dsds r r F r r o v v r r − − = ' ( ) ( ) 4 1 3 ( ) ' dldl r r F r r o l l r r − − =
Terminology for today Line density线密度 Surface density面密度 volume density体密度 Field intensity场强 field theory场论 Cartesian coordinate直角坐标系 magnitude模 ector矢量 Scalari标量 dot product点乘 cross product叉乘 tensor张量 Spinner旋量 gradient梯度 infinitesimal无限小 derivative微分 Partial derivative偏微 divergence散度 cur旋度 Operator算子 vector operator矢量算子 Laplace operator拉普拉斯 算子 Components分量 Stoke' s formula克托克斯公式
Terminology for today Line density 线密度 Surface density 面密度 volume density 体密度 Field intensity 场强 field theory场论 Cartesian coordinate 直角坐标系 magnitude 模 vector 矢量 Scalar标 量 dot product点乘 cross product 叉乘 tensor 张量 Spinner旋量 gradient 梯度 infinitesimal 无限小 derivative 微分 Partial derivative 偏微 divergence 散度 curl 旋度 Operator 算子 vector operator 矢量算子 Laplace operator 拉普拉斯 算子 Components 分量 Stoke’s formula 克托克斯公式
1. 2 Electric field intensity Discussion: Originally, the concept of field was introduced by the Convenience of treatment. It was later found out that the field does exist 1.2.1 Definition: E Test charge Q would not alter the field 1.2.2E produced by different shape of charges 1)Point shape charge E=∑ 2)Linear shape charge E=1,A(F)0 4 兀E
1. 2 Electric field intensity Discussion: Originally , the concept of field was introduced by the Convenience of treatment. It was later found out that the field does exist. 1.2.1.Definition: Q F E = 1.2.2 E produced by different shape of charges r dl r r E l 0 2 0 ( ) 4 1 = 2) Linear shape charge: 1)Point shape charge: 0 1 2 i n i i i r r Q E = = Test charge Q would not alter the field
3. Surface shape o(r E 4 丌E 4. Volume shape E 4 2 丌 Discussion: Although the introduction of Field intensity has greatly simplified the theory, in practice, vector calculation is still not that easy People hope the scalar can be used in analyzing the electric field Therefore, the chain will be: Electric field- Electric field intensity-??(?? Should be a scalar It is the time back to mathematics 1.2. 3 Brief Review of Vector Theory
3. Surface shape: ds r E r r o o s 2 ( ) 4 1 = 4. Volume shape: dv r E r r o o v 2 ( ) 4 1 = Discussion: Although the introduction of Field intensity has greatly simplified the theory, in practice, vector calculation is still not that easy. People hope the scalar can be used in analyzing the electric field. Therefore, the chain will be: Electric field → Electric field intensity→ ?? (?? Should be a scalar) It is the time back to Mathematics 1.2.3 Brief Review of Vector Theory
1)Vector in Cartesian coordinate A=A i+Aj+Ak 2)Magnitude of vector A=、A2+A2+ 3)Sum and subtraction 4)Multiplication Dot product AB=AB+AB,+A B=AB cos Cross product k V×A=
1) Vector in Cartesian coordinate A A i A j A k x y z = + + 2) Magnitude of vector 3) Sum and subtraction 4) Multiplication Dot product: Cross product: A• B = Ax Bx + Ay By + Az Bz = ABcos Ax Ay Az x y x i j k A = 2 2 2 A = Ax + Ay + Az