C=QV{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="C = Q / V" style="vertical-align:-17px;height:47px;width:53px">
- 地点:
- C=电容(F)
- 问=电荷(C)
- V=潜在的差异(V)
- 球形导体表面的电荷可以看作是点电荷在中心
- 潜在的V孤立点电荷的值为:
V=Q4πε0R{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="V等于分子Q除以分母4直的下标斜体0r的结束分数" style="vertical-align:-23px;height:53px;width:91px">
- 地点:
- 电荷Q是不电容器本身的电荷,就是储存的电荷在表面球形导体
- 将这些方程结合起来,可以得到孤立球体的电容表达式:
V=Q4πε0R=QC{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="V等于分子Q除以分母4直的下标斜体0r端分数等于Q除以C" style="vertical-align:-23px;height:53px;width:130px" loading="lazy">
C= 4πε0R
(部分)
第一步:列出已知的数量
-
- 球面半径,R= 75厘米= 75 × 10−2米
- 自由空间的介电常数,ε0= 8.85 × 10−12F m−1
第二步:写出带电球的电容方程
C= 4πε0R
步骤3:计算电容
C= 4π × (8.85 × 10−12) × (75 × 10−2)
C= 8.34 × 10−11F
部分(b)
第一步:列出已知的数量
-
- 原始的潜力,V1= 1.5 mv = 1.5 × 106V
- 最终电位=V2
- 原始能量=E1
- 最后的能量,E2= 0.05E1
第二步:写出电容器储存能量的方程
E=12CV2{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="E = 1 / 2cv²" style="vertical-align:-17px;height:47px;width:80px" loading="lazy">
第三步:写出放电前后的能量方程
E1=12CV12{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="E下标1等于1 / 2 C V下标1的平方" style="vertical-align:-17px;height:47px;width:95px" loading="lazy">
E2=12CV22{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="E下标2等于1 / 2 C V下标2的平方" style="vertical-align:-17px;height:47px;width:95px" loading="lazy">
第四步:使两个表达式相等并化简
12CV22=0.0512CV12{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="1 / 2cv下标2的平方等于0.05开括号1 / 2cv下标1的平方闭括号" style="vertical-align:-17px;height:47px;width:180px" loading="lazy">
V22 = 0.05V12{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="V下标2平方空格等于0.05开括号V下标1平方闭括号" style="vertical-align:-12px;height:29px;width:126px" loading="lazy">
V2 = 0.05 V1{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="V下标2空间等于空间的平方根0.05底根空间V下标1" style="vertical-align:-12px;height:32px;width:122px" loading="lazy">
第五步:计算最终电位,V2
V2=0.05{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="0.05的平方根" style="vertical-align:-6px;height:26px;width:51px" loading="lazy">×(1.5×106) = 3.35×105V