《大学物理第9章习题课选讲例题.ppt

有宽度为a的直长均匀带电薄板，沿 长度方向单位长度的带电量为l ， 试求：与 板的边缘距离为b的一点P 处的电场强度。 a P b . Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. r E l ε π 2 0 = d E d r l ε π 2 0 = a P b . d r r l a = d l d r r ε π 2 0 = l a d r E d d r l ε π 2 0 = E d ò = E a l ε π 2 0 = ò r d r a a+b = a l ε π 2 0 ln b a+b 解： Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 有一半径为 a 的非均匀带电的半 圆环，电荷线密度为l =l 0cosq 。 试求：圆心处 o 点的电场强度。 a y x o q Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. d π q r 2 ε 4 0 E d = q r = l 0cosq d d q = l d l π r 2 ε 4 0 = q r l 0cosq d Ex ò Ex = d q cos = ò E d π r 2 ε 4 0 q r l d q 2 cos 0 π 0 = ò π r ε 4 0 q l d q 2 cos 0 π 0 = ò + q 2 q sin 2 4 1 π 0 π r ε 4 0 l 0 = r ε 8 0 l 0 = r y x o q q d dE + + + + + + d l q l =l 0cosq 解： Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Ey ò Ey = d q sin = ò E d π r ε 4 0 l q 2 sin 0 = 2 π 0 =0 π r 2 ε 4 0 q r l d q cos 0 π 0 = ò q sin Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 有一半球面，半径为R，面上均 匀带电，电荷面密度为σ ， 尺寸如图所示。 求球心处o点的电场强度。 R o σ Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. E x 2 q ε π 4 0 + = ( ) a 2 2 3 x d E x 2 q ε π 4 0 + = ( ) a 2 2 3 x d 解： q d = σ R d π 2 l q cos x = sin q R a = cos q R 2 ε π 4 0 + = ( ) 2 2 3 σ R d π 2 l q sin cos q R . sin q R cos q R 2 2 ε 2 = σ q sin cos q R R d q . ε 2 0 σ q sin cos q d q E = π ò 2 0 ε 4 0 σ = q d q d x x R a Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 例6 无限大均匀带电平面的电场强