- 在球内部 ( r<R ) ,场强E=0,电势U与球面相同(与r无关)
- 空腔内无电荷,电荷分布在外表面上(内表面无电荷)
- 球壳实部场强E=0
- 磁力矩Pm与磁场B方向一致时稳定
第11章
- 毕奥萨法尔定律:dB=4πμ0r2Idl×e 不均匀磁场:B=∫dB
- 运动电荷的磁场:dB=4πμ0r2qv×e
- 磁场的高斯定理:∮SB⋅dS=0
- 安培环路定理:∮lB⋅dl=μ0∑I
![](data:image/png;base64,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)
重要结论:B=4πaμ0I(cosθ1−cosθ2)
(a :θ1顶点到θ2顶点的距离)
(θ1:起始端与电流方向夹角)
(θ2:末端与电流方向夹角)
无线长载流直导线:B=2πaμ0I
直导线延长线:B=0
![](data:image/png;base64,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)
圆电流轴线上某点的磁场:B=2(R2+x2)23μ0IR2
圆心处磁场:B=2Rμ0I
载流圆弧,圆心角θ:B=2Rμ0I⋅2πθ
长直载流螺线管内:B=μ0nI
磁场强度矢量:H=μrμ0B μ=μrμ0(磁导率)
半径为R的无限长均匀载流圆柱形导体内的磁场分布
半径为R的空心圆筒形导体内外的磁场分布
麦克斯韦方程组
电场的性质
由静电场中的高斯定理:∮sE静⋅