Re: [理工] [電磁] 力矩證明

看板Grad-ProbAsk作者youmehim (巧克力中毒)時間15年前 (2011/03/19 03:41)推噓1(1推 0噓 0→)

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※ 引述《ghjk918171 (匿名)》之銘言： : 書上寫到dipole在均勻電場與不均勻電場的力矩不同 : 在均勻電場τ=p cross E : 在不均勻電場τ=(p cross E)+(r cross F) : 想請問要如何證明在不均勻電場τ=(p cross E)+(r cross F) ??? → A dipole is placed at r in the electric field. → → The dipole moment is defined by p ≡ q * d , and the torque → → → → → → → τ = Σ r_i ×F_i = r_- ×( -q * E_- ) + r_+ ×( +q * E_+ ) i with → → → r_+ = r + d/2 → → → r_- = r - d/2 → → E_+ / E_- are the electric fields at +q / -q . so → → → → → → → τ = ( r - d/2 ) ×( -q * E_- ) + ( r + d/2 ) ×( +q * E_+ ) → → → → → → = r ×[ ( -q * E_- ) + ( +q * E_+ ) ] + d ×[ q * ( E_+ + E_- )/2 ] → → → → → = r ×F + p ×( E_+ + E_- )/2 → → → For a ideal dipole, d → 0, and then ( E_+ + E_- )/2 approximates to → the electric field E at the position of the dipole. finally → → → → → τ = r ×F + p ×E ＃ -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 140.112.230.114

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