soluzioni numeriche esercizi

SOLUZIONINUMERICHEESERCIZI

Dott.ssa Elisabetta Bissaldi

Capitolo 0

Es. 0.1

1. 𝒂 = 𝟗. 𝟖𝟑 𝒎/𝒔𝟐

Es. 0.2

1. 𝒗𝑭 = 𝟔 × 𝟏𝟎𝟒 𝒎/𝒔 = 𝟔𝟎 𝒌𝒎/𝒔 = 𝟐. 𝟐 × 𝟏𝟎𝟓𝒌𝒎/𝒉

Es. 0.3

1. 𝑴 =𝟒𝝅𝟐𝒓𝟑

𝜸T𝟐

2. 𝑬𝒎 = −𝜸𝒎𝑴

𝟐𝒓=

𝑬𝑷

𝟐

3. 𝑻 = 𝟐𝝅𝒓𝟑

𝜸𝑴𝑻 = 𝟖𝟔. 𝟓 𝒎𝒊𝒏 𝟏𝟎𝟎 𝒌𝒎 ; 𝑻 = 𝟗𝟎𝒎𝒊𝒏 (𝟑𝟎𝟎 𝒌𝒎)

Elisabetta Bissaldi (Politecnico di Bari) - A.A. 2020-2021 2

Capitolo 1

Es. 1.1

1. 𝒙 = 𝟏. 𝟓 𝒄𝒎

2. 𝜽 = 𝟎. 𝟒°

Es. 1.2

1. 𝒙 = 𝟐 𝑳

Es. 1.3

1. 𝑭 =𝒒𝟐 𝟑

𝟒𝝅𝜺𝟎𝒍𝟐 ෝ𝒖𝒚

2. 𝑬𝑻𝑶𝑻 = 𝟎


Capitolo 1

Es. 1.4

1. 𝑬𝒙 𝒙 =𝒒

𝟒𝝅𝜺𝟎

𝒙

𝑹𝟐+𝒙𝟐𝟑/𝟐 ෝ𝒖𝒙, 𝑬𝒚 = 𝟎, 𝑬𝒛 = 𝟎

Es. 1.5

1. 𝑬𝒙(𝒙) =𝝈

𝟐𝜺𝟎𝟏 −

𝒙

𝑹𝟐+𝒙𝟐ෝ𝒖𝒙, 𝑬𝒚 = 𝟎, 𝑬𝒛 = 𝟎

• Per 𝒙 → 𝟎 e per 𝑹 → ∞➔𝑬+ =𝝈

𝟐𝜺𝟎ෝ𝒖𝒙 𝑬− = −

𝝈

𝟐𝜺𝟎ෝ𝒖𝒙

Es. 1.6

1. 𝑬 =𝝈

𝜺𝟎ෝ𝒖𝒙 (per 𝐱𝟏 < 𝒙 < 𝒙𝟐)

• Per 𝒙 < 𝒙𝟏 e per 𝒙 > 𝒙𝟐 ➔ 𝑬 = 𝟎

2. 𝑬+ =𝝈

𝟐ෝ𝒖𝒙 𝑬− = −

𝝈

𝟐ෝ𝒖𝒙Elisabetta Bissaldi (Politecnico di Bari) - A.A. 2020-2021 4

Capitolo 1

Es. 1.7

1. 𝒙 𝒕 =𝟏

𝟐𝒂 𝒕𝟐 =

𝒒𝑬

𝟐𝒎𝒕𝟐, 𝒗 𝒕 = 𝒂𝒕 =

𝒒𝑬

𝒎𝒕

2. 𝚫𝑬𝒌 = 𝒒𝑬𝒙

Es. 1.8

• 𝑭𝟏 = 𝑭𝟏 ෝ𝒖𝒙, 𝑭𝟏 = 𝟕. 𝟐 × 𝟏𝟎−𝟔 𝑵

• 𝑭𝟐 = 𝑭𝟐 ෝ𝒖𝒙, 𝑭𝟐 = 𝟏. 𝟒 × 𝟏𝟎−𝟓 𝑵

• 𝑭𝟑 = −𝑭𝟑ෝ𝒖𝒙, 𝑭𝟑 = 𝟐. 𝟐 × 𝟏𝟎−𝟓 𝑵

Es. 1.9

• 𝑭𝟑 = −𝑭𝒙 ෝ𝒖𝒙 −𝑭𝒚 ෝ𝒖𝒚, 𝑭𝒙 = 𝟐. 𝟓 × 𝟏𝟎−𝟔𝑵,𝑭𝒚 = 𝟑 × 𝟏𝟎−𝟓𝑵

• 𝑭𝟑 = 𝟑 × 𝟏𝟎−𝟓𝑵, 𝜽𝑭𝟑 = −𝟖𝟓°


Capitolo 1

Es. 1.10

• 𝑭𝟒 = 𝑭𝒙 ෝ𝒖𝒙 + 𝑭𝒚 ෝ𝒖𝒚, 𝑭𝒙 = 𝟏. 𝟒 × 𝟏𝟎−𝟒𝑵,𝑭𝒚 = −𝟒 × 𝟏𝟎−𝟒𝑵

• 𝑭𝟒 = 𝟒. 𝟐 × 𝟏𝟎−𝟒𝑵, 𝜽𝑭 = −𝟕𝟏°

Es. 1.11

1. 𝑭𝒕𝒐𝒕 = (−𝟔. 𝟓 × 𝟏𝟎−𝟓𝑵)ෝ𝒖𝒙

2. 𝑭𝒕𝒐𝒕 = 𝟏. 𝟗 × 𝟏𝟎−𝟓𝑵 ෝ𝒖𝒚

Es. 1.12

• 𝑬𝑨 = 𝑬𝒙 ෝ𝒖𝒙 + 𝑬𝒚 ෝ𝒖𝒚, 𝑬𝒙 = 𝟏. 𝟏 × 𝟏𝟎𝟔𝑵/𝑪, 𝑬𝒚 = 𝟒. 𝟒 × 𝟏𝟎𝟔𝑵/𝑪

• 𝑬𝑨 = 𝟒. 𝟓 × 𝟏𝟎𝟔𝑵/𝑪, 𝜽𝑭 = 𝟕𝟔°


Capitolo 1

Es. 1.13

1. 𝒒𝟏 = 𝟑. 𝟖 × 𝟏𝟎−𝟓𝑪, 𝒒𝟐 = 𝟏. 𝟐 × 𝟏𝟎−𝟓𝑪

Es. 1.14

1. 𝑬𝑷(𝒓) =𝟑𝝀

𝟒𝝅𝜺𝟎𝒓ෝ𝒖𝒙

Es. 1.15

1. 𝑸𝟏/𝟐 = 𝟐 × 𝟏𝟎−𝟏𝟏𝑪

2. 𝑬𝑶 = −𝑨

𝟒𝜺𝟎𝑹ෝ𝒖𝒚


Capitolo 1

Es. 1.16

1. 𝑬 𝒂 = −𝟏

𝟒𝝅𝜺𝟎

𝒒

𝒂 𝒂+𝑳ෝ𝒖𝒙

Es. 1.17

• 𝑬𝑷 = −𝑬𝟏 ෝ𝒖𝒙 − 𝑬𝟐 ෝ𝒖𝒚, 𝑬𝑷 = 𝟒𝟐. 𝟒 𝑵/𝑪, 𝜽𝑭 = −𝟒𝟓°

Es. 1.18

1. 𝑬 𝒚 =𝝀

𝟐𝝅𝜺𝟎𝒚𝒔𝒆𝒏𝝓 ෝ𝒖𝒚

2. 𝑬 𝒚 𝑳→∞ =𝝀

𝟐𝝅𝜺𝟎𝒚ෝ𝒖𝒚, 𝑬 𝒚 𝑳→𝟎 =

𝝀𝑳

𝟒𝝅𝜺𝟎𝒚𝟐 ෝ𝒖𝒚


Capitolo 2

Es. 2.1

1. 𝑽𝑪 =𝟑 𝟑 𝒒

𝟒𝝅𝜺𝟎𝒍

Es. 2.2

1. 𝑼𝒆 𝒔𝒊𝒔𝒕𝒆𝒎𝒂 =𝟑𝒒𝟐


2. 𝑾 = 𝑼𝒆 𝒒𝟎 = 𝒒𝟎𝑽𝑪 =𝟑 𝟑𝒒𝟎𝒒


Es. 2.3

1. 𝑽 𝒙 =𝒒

𝟒𝝅𝜺𝟎

𝟏

𝑹𝟐+𝒙𝟐, 𝑬𝒙 𝒙 = −

𝝏𝑽

𝝏𝒙ෝ𝒖𝒙


Capitolo 2

Es. 2.4

1. 𝑽 𝒙 =𝝈

𝟐𝜺𝟎𝑹𝟐 + 𝒙𝟐 − 𝒙 , 𝑬𝒙 𝒙 = −

𝝏𝑽

𝝏𝒙ෝ𝒖𝒙

Es. 2.5

1. 𝚫𝐕 = 𝐕𝟎 − 𝑽 𝒙 =𝝈

𝜺𝟎(𝒙 − 𝒙𝟎) =

𝝈

𝜺𝟎𝒉

Es. 2.6

1. 𝑽𝑪 = 𝟑𝟓𝟎 𝑽


Capitolo 2

Es. 2.7

1. 𝑽 𝒅 =𝝀

𝟒𝝅𝜺𝟎𝒍𝒏

𝑳+ 𝑳𝟐+𝒅𝟐

𝒅

Es. 2.8

1. 𝑾𝒕𝒐𝒕 =𝒒𝟐

𝟒𝝅𝜺𝟎𝒍𝟐 − 𝟒

Es. 2.9

1. 𝒗 = 𝟕𝟎𝟎𝟎𝒎/𝒔


Capitolo 2

Es. 2.10

1. 𝑾 = 𝟎. 𝟏𝟖 𝒏𝑱

Es. 2.11

1. 𝑽 𝒓 < 𝑹 = −𝝆𝒓𝟐

𝟔𝜺𝟎= −

𝒒𝒓𝟐

𝟖𝝅𝜺𝟎𝑹𝟑

2. 𝑽 𝒓 < 𝑹 =𝝆

𝟔𝜺𝟎𝟑𝑹𝟐 − 𝒓𝟐 =

𝒒

𝟖𝝅𝜺𝟎𝑹𝟑 𝟑𝑹𝟐 − 𝒓𝟐

Es. 2.12

1. 𝑽 𝒅/𝟐 = −𝟏𝟖𝟎 𝑽

2. 𝑽𝑺𝟏 = 𝟐𝟖𝟔𝟓 𝑽, 𝑽𝑺𝟐 = −𝟖𝟗𝟓𝟓 𝑽


Capitolo 2

Es. 2.13

1. 𝑹 = 𝟗𝟎 𝒄𝒎

2. 𝑸 = 𝟒𝟎 𝒏𝑪

Es. 2.14

1. 𝚫E𝒌 = 𝒆𝑬𝒉 = 𝟏. 𝟔 × 𝟏𝟎−𝟏𝟓 𝑱

2. 𝒗 = 𝟓. 𝟗 × 𝟏𝟎𝟕 𝒎/𝒔

Es. 2.15

1. 𝑾 = −𝟑. 𝟔 × 𝟏𝟎−𝟔 𝑱


Capitolo 3

Es. 3.1

1. 𝑬 𝒓 < 𝑹 = 𝟎, 𝑬 𝒓 > 𝑹 =𝒒

𝟒𝝅𝜺𝟎𝒓𝟐 ෝ𝒖𝒓 =

𝝈𝑹𝟐

𝜺𝟎 𝒓𝟐 ෝ𝒖𝒓

2. 𝑽 𝒓 < 𝑹 = 𝑽 𝑹 =𝒒

𝟒𝝅𝜺𝟎𝑹= 𝒄𝒐𝒔𝒕𝒂𝒏𝒕𝒆, 𝑽 𝒓 > 𝑹 =

𝒒

𝟒𝝅𝜺𝟎𝒓

Es. 3.2

1. 𝑬 𝒓 > 𝑹 =𝒒

𝟒𝝅𝜺𝟎𝒓𝟐 ෝ𝒖𝒓 =

𝝆𝑹𝟑

𝟑 𝜺𝟎 𝒓𝟐 ෝ𝒖𝒓, 𝑬 𝒓 < 𝑹 =

𝒒 𝒓

𝟒𝝅𝜺𝟎𝑹𝟑 ෝ𝒖𝒓 =

𝝆𝒓

𝟑 𝜺𝟎ෝ𝒖𝒓

2. 𝑽 𝒓 > 𝑹 =𝒒

𝟒𝝅𝜺𝟎𝒓, 𝑽 𝒓 < 𝑹 =

𝒒

𝟖𝝅𝜺𝟎𝑹𝟑 −

𝒓𝟐

𝑹𝟐=

𝝆

𝟔𝜺𝟎𝟑𝑹𝟐 − 𝒓𝟐


Capitolo 3

Es. 3.3

1. 𝑬 𝒓 =𝝀

𝟐𝝅𝜺𝟎𝒓ෝ𝒖𝒓

2. 𝑽 𝒓𝟏 − 𝑽 𝒓𝟐 =𝝀

𝟐𝝅𝜺𝟎𝒍𝒏

𝒓𝟐

𝒓𝟏

Es. 3.4

1. 𝑬 𝒙 > 𝟎 =𝝈

𝟐𝜺𝟎ෝ𝒖𝒙, 𝑬 𝒙 < 𝟎 = −

𝝈

𝟐𝜺𝟎ෝ𝒖𝒙

2. 𝑽 𝒙𝟏 − 𝑽 𝒙𝟐 =𝝈

𝟐𝜺𝟎𝒙𝟐 − 𝒙𝟏


Capitolo 3

Es. 3.5

1. 𝑬𝒆𝒔𝒕 = 𝟏. 𝟓 × 𝟏𝟎𝟒 𝑽/𝒎, 𝑬𝒊𝒏𝒕 = 𝟓 × 𝟏𝟎𝟑 𝑽/𝒎

2. 𝑽 𝒙 = −𝟐𝟎𝟎𝟎 𝑽

Es. 3.6

1. 𝑬 𝒓 < 𝒂 = 𝟎, 𝑬 𝒂 < 𝒓 < 𝒃 =𝝆(𝒓𝟑−𝒂𝟑)

𝟑𝜺𝟎𝒓𝟐 ෝ𝒖𝒓, 𝑬 𝒓 > 𝒃 =

𝝆(𝒃𝟑−𝒂𝟑)

𝟑𝜺𝟎𝒓𝟐 ෝ𝒖𝒓

2. 𝑬 𝒃 = 𝟔𝟔𝟎𝟎 𝑽/𝒎, 𝑬 𝒓 = 𝟑𝟑𝟑𝟎 𝑽/𝒎

Es. 3.7

1. 𝑽 = −𝟔𝟑𝟎𝟎 𝑽

2. 𝑾 = 𝟏𝟗𝒎𝑱


Capitolo 3

Es. 3.8

1. 𝝀 = 𝟓 𝝁𝑪/𝒎

Es. 3.9

1. 𝚽𝟏 𝑬 = 𝟖. 𝟐 𝑵𝒎𝟐/𝑪, 𝚽𝟐 𝑬 = 𝟏𝟔. 𝟐 𝑵𝒎𝟐/𝑪

2. 𝐪𝟏 = 𝟕𝟑 𝒑𝑪, 𝒒𝟐 = 𝟏𝟒𝟎 𝒑𝑪

Es. 3.10

1. 𝑬𝒂 = 𝟐. 𝟐𝟓 ⋅ 𝟏𝟎𝟔 𝑽/𝒎, 𝑬𝒃 = −𝟒. 𝟓 ⋅ 𝟏𝟎𝟓 𝑽/𝒎


Capitolo 3

Es. 3.11

1. 𝒉𝟎 = 𝟏𝟕. 𝟔 𝒄𝒎

2. 𝒗 = 𝟏. 𝟏𝟐 𝒎/𝒔

Es. 3.12

1. 𝑬𝒕𝒐𝒕 = 𝟐. 𝟐 ⋅ 𝟏𝟎−𝟏𝟖 𝑱 = 𝟏𝟑. 𝟔 𝒆𝑽


Capitolo 4

Es. 4.1

1. 𝒒𝟏 = 𝒒𝑹𝟏

𝑹𝟏+𝑹𝟐, 𝒒𝟐 = 𝒒

𝑹𝟐

𝑹𝟏+𝑹𝟐

Es. 4.2

1. 𝑪 = 𝟒𝝅𝜺𝟎𝑹𝟏

2. 𝑪 = 𝟖. 𝟖𝟓 𝒏𝑭

Es. 4.3

1. 𝑪 =𝜺𝟎𝚺

𝒉


Capitolo 4

Es. 4.4

1. 𝑪 = 𝟐𝝅𝜺𝟎𝒅/ 𝒍𝒏 𝑹𝟐/𝑹𝟏

Es. 4.5

1. 𝑪𝟏 = 𝟐𝟎𝟎 𝒑𝑭, 𝑪𝟐 = 𝟓𝟎𝟎 𝒑𝑭, 𝑪𝟑 = 𝟑𝟑𝟑 𝒑𝑭

Es. 4.6

1. 𝑽𝒌 =𝝈𝟎

𝜺𝟎𝒉 𝟏 −

𝒔

𝒉

𝒌−𝟏

𝒌

2.𝟏

𝑪𝒆𝒒=

𝒉−𝒔

𝜺𝟎𝚺+

𝒔

𝜺𝟎 𝐤 𝚺


Capitolo 4

Es. 4.7

1. .

a) 𝑫 𝒓 =𝒒

𝟒𝝅𝒓𝟐ෝ𝒖𝒓

b) 𝑬 𝒓 =𝒒

𝟒 𝝅 𝜺𝟎 𝒌 𝒓 𝟐ෝ𝒖𝒓

c) 𝑷 𝒓 =𝒌−𝟏

𝒌

𝒒

𝟒𝝅𝒓𝟐ෝ𝒖𝒓

2. 𝒒𝑷 = −𝒌−𝟏

𝒌𝒒

Es. 4.8

1. 𝑭 = 𝟔. 𝟔 ⋅ 𝟏𝟎−𝟓𝑵

2. 𝑾 = 𝟏. 𝟑𝟑 ⋅ 𝟏𝟎−𝟓𝑱

3. 𝑼𝒆 = 𝟐. 𝟔𝟔 ⋅ 𝟏𝟎−𝟓𝑱


Capitolo 4

Es. 4.9

1. 𝜟𝑽 = 𝟓. 𝟒 𝑽

Es. 4.10

2. 𝑸𝟐 = −𝟏 𝒏𝑪, 𝑸𝟑 = 𝟐 𝒏𝑪, 𝑸 = 𝟏 𝒏𝑪

3. 𝑽 𝑹𝟏 = 𝟑𝟎𝟎 𝑽

Es. 4.11

1. 𝒒𝒔𝒇𝒆𝒓𝒂 𝑹𝟏 = 𝟎, 𝒒𝒈𝒖𝒔𝒄𝒊𝒐 𝑹𝟐 = 𝟎, 𝒒𝒈𝒖𝒔𝒄𝒊𝒐 𝑹𝟑 = 𝟐𝟎 𝒏𝑪

2. 𝒒𝒈𝒖𝒔𝒄𝒊𝒐 𝑹𝟐 = −𝟐𝟎 𝒏𝑪, 𝒒𝒈𝒖𝒔𝒄𝒊𝒐 𝑹𝟑 = 𝟒𝟎 𝒏𝑪

3. 𝚫𝐕 = 𝟏𝟐𝟎𝟎 𝐕


Capitolo 4

Es. 4.12

1. 𝑸𝟏 = −𝟏 𝒏𝑪,𝑸𝟐 = 𝟑 𝒏𝑪

2. 𝑷𝒆𝒓 𝒓 < 𝑹𝟏: 𝑬 𝒓 =𝑸

𝟒𝝅𝜺𝟎𝒓𝟐

𝑷𝒆𝒓 𝑹𝟏 < 𝒓 < 𝑹𝟐: 𝑬 = 𝟎

𝑷𝒆𝒓 𝒓 > 𝑹𝟐: 𝑬 𝒓 =𝑸𝟐


3. 𝑽 𝑹𝑩 = 𝟏𝟓𝟎 𝑽, 𝑽 𝑹𝑨 = 𝟐𝟑𝟎 𝑽

Es. 4.13

1. 𝑷𝒆𝒓 𝒓 < 𝑹𝟏: 𝑬 = 𝟎

𝑷𝒆𝒓 𝑹𝟏 < 𝒓 < 𝑹𝟐: 𝑬 𝒓 =𝑸


𝑷𝒆𝒓 𝑹𝟐 < 𝒓 < 𝑹𝟑: 𝑬 = 𝟎

𝑷𝒆𝒓 𝒓 > 𝑹𝟑: 𝑬 𝒓 =𝑸


2. 𝑸𝟏 = 𝟏𝟎 𝒏𝑪3. 𝑸𝟏 = 𝟏𝟎 𝒏𝑪, 𝑸𝟐 = −𝟏𝟎 𝒏𝑪, 𝑸𝟑 = 𝟑𝟎 𝒏𝑪4. 𝑽 𝑹𝟑 = 𝟗𝟎𝟎 𝑽


Capitolo 4

Es. 4.14

1. 𝑸 = 𝟎. 𝟒 𝝁𝑪

2. 𝑸′ = 𝟎. 𝟐 𝝁𝑪

3. 𝑸𝟏 = −𝟎. 𝟐 𝝁𝑪

4. 𝑽 𝑷𝟐 = −𝟗𝟎𝟎 𝑽

Es. 4.15

1. 𝒒𝟏 = 𝒒𝟑 = 𝒒𝟓 = 𝟒 𝒏𝑪, 𝒒𝟐 = 𝒒𝟒 = −𝟒 𝒏𝑪

3. 𝚫𝐕𝟏,𝟓 = 𝟐𝟏𝟎𝟎 𝑽

4. 𝑼𝒆 = 𝟓. 𝟔 𝝁𝑱

5. 𝑼𝒆′ = 𝟒. 𝟐 𝝁𝑱


Capitolo 4

Es. 4.16

1. 𝑸 = 𝟒 𝒏𝑪, 𝑸′ = 𝟔. 𝟔 𝒏𝑪

2. 𝑷𝒆𝒓 𝒓 < 𝑹𝟐 𝑬 = 𝟎, 𝑷𝒆𝒓 𝒓 ≥ 𝑹𝟐 𝑬 𝒓 =𝑸′


3. 𝑽 =𝑸′

𝟒𝝅𝜺𝟎𝑹𝟐= 𝟑𝟎𝟎 𝑽

Es. 4.17

1. 𝑷𝒆𝒓 𝒓 < 𝑹 𝑬 𝒓 =𝑸𝒓

𝟒𝝅𝜺𝟎𝒌𝑹𝟑 =

𝝆𝒓

𝟑𝜺𝟎𝒌, 𝑷𝒆𝒓 𝒓 ≥ 𝑹 𝑬 𝒓 = 𝟎

𝑷𝒆𝒓 𝒓 < 𝑹 𝑽 𝒓 =𝑸

𝟖𝝅𝜺𝟎𝒌𝑹𝟑𝑹𝟐 − 𝒓𝟐 =

𝝆𝒓

𝟔𝜺𝟎𝒌𝑹𝟐 − 𝒓𝟐 ,

𝑷𝒆𝒓 𝒓 ≥ 𝑹 𝑽 𝒓 = 𝟎

2. 𝝈𝟎 =𝑸

𝟒𝝅𝑹𝟐(𝒏𝒆𝒈𝒂𝒕𝒊𝒗𝒂 𝒔𝒆 𝑸 𝒑𝒐𝒔𝒊𝒕𝒊𝒗𝒂)

3. 𝝈𝑷 =𝒌−𝟏

𝒌

𝑸

𝟒𝝅𝑹𝟐


Capitolo 4

Es. 4.18

1. 𝑷𝒆𝒓 𝒓 < 𝑹𝟏: 𝑬 = 𝟎

𝑷𝒆𝒓 𝑹𝟏 < 𝒓 < 𝑹𝟐: 𝑬 𝒓 =𝑸


𝑷𝒆𝒓 𝑹𝟐 < 𝒓 < 𝑹𝟑: 𝑬 𝒓 =𝑸

𝟒𝝅𝜺𝟎𝒌 𝒓𝟐

𝑷𝒆𝒓 𝒓 > 𝑹𝟑: 𝑬 𝒓 =𝑸


2. 𝑼𝒆 = 𝟏. 𝟗 ⋅ 𝟏𝟎𝟓 𝑱

Es. 4.19

1. 𝑸𝟎 = 𝑸𝟏 = 𝟏. 𝟔 𝒏𝑪, 𝑸𝟐 = 𝟏 𝒏𝑪

2. 𝚫𝐕𝟎 = 𝟖𝟎 𝑽, 𝚫𝑽𝟏 = 𝟐𝟎 𝑽


Capitolo 4

Es. 4.20

1. 𝑸𝒇,𝟏 = 𝟔. 𝟕 𝒏𝑪, 𝑸𝒇,𝟐 = 𝟏𝟑. 𝟑 𝒏𝑪, 𝑸𝒇,𝑻𝑶𝑻 = 𝟐𝟎 𝒏𝑪

2. 𝚫𝐕′ = 𝟔𝟔. 𝟕 𝑽

3. 𝑼𝑭 = 𝟎. 𝟔𝟕 𝝁𝑱

Es. 4.21

1. 𝑪𝒌 = 𝟓𝟎 𝒏𝑭

2. 𝒒𝑷 = 𝟒 𝝁𝑪

3. 𝑸 = 𝟓 𝝁𝑪


Capitolo 4

Es. 4.22

1. 𝑪𝒆𝒒 = 𝟐𝟔. 𝟔 𝒑𝑭

2. 𝐤 = 𝟓

3. 𝑬 = 𝟑 ⋅ 𝟏𝟎𝟒𝑽

𝒎

4. 𝑫𝑽 = 𝝈𝟎,𝑽 = 𝟎. 𝟐𝟕 𝝁𝑪/𝒎𝟐, 𝐃𝐃 = 𝝈𝟎,𝑫 = 𝟏. 𝟑 𝝁𝑪/𝒎𝟐

Es. 4.23

1. 𝒌 = 𝟏𝟏

2. 𝑾 = 𝟕𝟓 𝝁𝑱


Capitolo 4

Es. 4.24

1. 𝑸 = 𝟕𝟖. 𝟒 𝒏𝑪

2. 𝑪𝒆𝒒 = 𝟏𝟗𝟕 𝒑𝑭

3. 𝑬𝟎 = 𝟖. 𝟖 ⋅ 𝟏𝟎𝟒 𝑽/𝒎, 𝑬𝒌 = 𝟐. 𝟐 ⋅ 𝟏𝟎𝟒 𝑽/𝒎, 𝑬𝒊𝒏𝒕 = 𝟎

Es. 4.25

1. 𝝈𝟏 = 𝟎. 𝟔𝟔 𝝁𝑪/𝒎𝟐, 𝝈𝟐 = 𝟏. 𝟑 𝝁𝑪/𝒎𝟐

2. 𝑬𝟏 = 𝟕. 𝟓 ⋅ 𝟏𝟎𝟒 𝑽/𝒎, 𝑬𝟐 = 𝟏. 𝟓 ⋅ 𝟏𝟎𝟓 𝑽/𝒎

3. 𝑬𝟏 = 𝟑 ⋅ 𝟏𝟎𝟒𝑽

𝒎, 𝑬𝟐 = 𝟓. 𝟖 ⋅ 𝟏𝟎𝟒 𝑽/𝒎,

𝑫𝟏 = 𝟎. 𝟓𝝁C

𝒎𝟐 , 𝑫𝟐 = 𝟏. 𝟓 𝝁𝑪/𝒎𝟐


Capitolo 4

Es. 4.26

1. 𝑪𝟎 = 𝟖. 𝟖𝟓 𝒑𝑭, 𝑪𝒆𝒒 = 𝟏𝟒. 𝟔 𝒑𝑭

2. 𝑬𝟎 = 𝟒 ⋅ 𝟏𝟎𝟒𝑽

𝒎, 𝑬𝒌 = 𝟏. 𝟑 ⋅ 𝟏𝟎𝟒 𝑽/𝒎

3. 𝝈𝑷𝟏 = −𝟎. 𝟐𝟑 𝝁𝑪 /𝒎𝟐, 𝝈𝑷𝟐 = 𝟎. 𝟐𝟑 𝝁𝑪 /𝒎𝟐

Es. 4.27

1. 𝑪𝒆𝒒 = 𝟔𝟏𝟗 𝒑𝑭

2. 𝑼𝟏 = 𝟎. 𝟑𝟓 𝒎𝑱,𝑼𝟐 = 𝟎. 𝟖𝟖 𝒎𝑱

3. 𝑸𝟏 = 𝟎. 𝟑𝟓 𝝁𝑪, 𝑸𝟐 = 𝟎. 𝟖𝟖 𝝁𝑪

4. 𝑬𝟏 = 𝑬𝟐 = 𝟏𝟎𝟔 𝑽/𝒎


Capitolo 4

Es. 4.28

1. 𝝈𝟏 = −𝟎. 𝟑 𝝁𝑪 /𝒎𝟐, 𝝈𝟐 = 𝟎. 𝟏𝟔 𝝁𝑪 /𝒎𝟐

𝑬𝟏 = 𝟏𝟐𝟎𝟎 𝑽/𝒎, 𝑬𝟐 = 𝟔𝟎𝟎𝟎 𝑽/𝒎

2. 𝜟𝑽 = 𝟒𝟎 𝑽

3. 𝒒𝑷 = 𝟏. 𝟑𝟑 𝒏𝑪

Es. 4.29

1. 𝚫𝐐 = 𝟎. 𝟏𝟑 𝝁𝑪

2. 𝚫𝐕𝟏′ = 𝟏𝟑𝟑 𝑽

3. 𝑾𝒈𝒆𝒏 = 𝟓𝟑 𝝁𝑱


Capitolo 4

Es. 4.30

2. 𝒌 = 𝟑

3. 𝝈𝑷𝟏 = −𝟐𝟏 𝒏𝑪 /𝒎𝟐, 𝝈𝟐 = 𝟐. 𝟑 𝒏𝑪 /𝒎𝟐

4. 𝑽 𝒍 = 𝟑𝟎 𝑽

Es. 4.31

2. 𝑸 = 𝟑 𝒏𝑪

3. 𝒌 = 𝟑

4. 𝚫𝐕 = 𝟐𝟓 𝐕


Capitolo 5

Es. 5.1

1. 𝒗 = 𝟏. 𝟒𝟕 ⋅ 𝟏𝟎−𝟒 𝒎/𝒔

Es. 5.2

1. 𝐄 = 𝟑. 𝟑𝟒 ⋅ 𝟏𝟎−𝟐 𝑽/𝒎

2. 𝝉 = 𝟐. 𝟓 ⋅ 𝟏𝟎−𝟏𝟒𝒔, 𝒍 = 𝟑. 𝟗𝟕 ⋅ 𝟏𝟎−𝟖 𝐦

Es. 5.3

1. 𝑹𝒆𝒒 = 𝟖. 𝟕 𝛀

2. 𝑷 = 𝟑𝟓𝑾

3. 𝚫V = 𝟓. 𝟒 𝑽

4. 𝒊𝟏 = 𝟏. 𝟖 𝑨, 𝒊𝟐 = 𝟎. 𝟐 𝑨


Capitolo 5

Es. 5.4

1. 𝑽𝑫𝑩 = 𝟐𝟎 𝑽

2. 𝑽𝑪𝑫 = 𝟐𝟓 𝑽

3. 𝑽𝑨𝑪 = 𝟓𝟎 𝑽

4. 𝑽𝑨𝑩 = 𝟗𝟓 𝑽

Es. 5.5

1. 𝐝 = 𝟎. 𝟎𝟑𝟖 𝐜𝐦

Es. 5.6

1. 𝐑 = 𝟓𝟒 𝛀


Capitolo 5

Es. 5.7

1. 𝒍 = 𝟓. 𝟖𝟓 𝒎

Es. 5.8

1. 𝑰 = 𝑱𝟎𝚺/𝟑

Es. 5.9

1. 𝐏 = 𝟐. 𝟖𝟓 𝐤𝐖

2. 𝐒𝐩𝐞𝐬𝐚 = 𝟏. 𝟒𝟐 𝐞𝐮𝐫𝐨

Es. 5.10

1. 𝐥 = 𝟓. 𝟖𝟓 𝐦

2. 𝒍′ = 𝟏𝟎. 𝟒 𝒎


Capitolo 5

Es. 5.11

1. 𝑾𝒇 = 𝟏𝟎. 𝟔 𝒌𝑱

Es. 5.12

1. 𝐑 = 𝟖 𝛀

Es. 5.13

1. 𝒋 = 𝟓. 𝟏 ⋅ 𝟏𝟎𝟔𝑨 /𝒎𝟐

2. 𝑬 = 𝟎. 𝟎𝟖𝟕 𝑽/𝒎

3. 𝚫𝐕 = 𝟐𝟔 𝐕

4. 𝑷 = 𝟔𝟓𝟑𝑾


Capitolo 6

Es. 6.1

1. 𝑭𝑹 = 𝟐𝒊𝑹𝑩 ෝ𝒖𝒛, 𝑭𝑪 = −𝟐𝒊𝑹𝑩 ෝ𝒖𝒛 → 𝑭𝑻𝑶𝑻 = 𝟎

Es. 6.2

1. 𝒗 = 𝟏. 𝟑 ⋅ 𝟏𝟎𝟕 𝒎/𝒔

2. 𝑩 = 𝟓. 𝟓 ⋅ 𝟏𝟎−𝟒 𝑻

Es. 6.3

1. 𝑩 = 𝟏. 𝟔 ⋅ 𝟏𝟎−𝟐 𝑻


Capitolo 6

Es. 6.4

1. 𝑩 = 𝟐. 𝟕 ⋅ 𝟏𝟎−𝟒𝑻

Es. 6.5

1. 𝑴 = 𝟓 ⋅ 𝟏𝟎−𝟑 𝑵𝒎


Capitolo 7

Es. 7.1

1. 𝑩 = 𝟔. 𝟖 ⋅ 𝟏𝟎−𝟔 𝑻

Es. 7.2

1. 𝐏𝐞𝐫 𝐫 > 𝐑: 𝑩(𝒓) =𝝁𝟎 𝒊

𝟐𝝅𝒓

𝐏𝐞𝐫 𝐫 < 𝐑: 𝑩(𝒓) =𝝁𝟎 𝒊 𝒓

𝟐 𝝅𝑹𝟐

Es. 7.3

1. 𝑩 = 𝝁𝟎 𝒏 𝒊


Capitolo 7

Es. 7.4

1. 𝑩 𝒓 =𝝁𝟎 𝑵 𝒊

𝟐𝝅 𝒓

Es. 7.5

1. 𝑩 𝒅 = 𝟐 ⋅ 𝟏𝟎−𝟓 𝑻

Es. 7.6

1. 𝑩𝑻𝑶𝑻 = 𝟑 ⋅ 𝟏𝟎−𝟓 𝑻 diretto lungo asse x positivo


Capitolo 7

Es. 7.7

1. 𝒊 = 𝟓. 𝟐 𝑨

Es. 7.8

1. 𝒅 = 𝟖. 𝟐 𝒎𝒎

Es. 7.9

1. 𝑩 𝒙 =𝝁𝟎𝑰

𝟐𝝅𝒙

2. 𝑭 = −𝟏𝟎−𝟕 𝑵

3. 𝚽 𝑩 = 𝟏. 𝟒 × 𝟏𝟎−𝟗 𝑾𝒃


Capitolo 7

Es. 7.10

1. 𝑻𝒓𝒂𝒊𝒆𝒕𝒕𝒐𝒓𝒊𝒂 𝒄𝒊𝒓𝒄𝒐𝒍𝒂𝒓𝒆

2. 𝑭𝒆 = 𝟒 × 𝟏𝟎−𝟏𝟐 𝑵, diretta lungo asse z negativo

3. 𝑹 = 𝟓. 𝟕 × 𝟏𝟎−𝟔 𝒎

4. 𝑻 = 𝟕. 𝟏𝟓 × 𝟏𝟎−𝟏𝟐 𝒔

Es. 7.11

1. 𝑩𝑻𝑶𝑻 = 𝟏. 𝟐 × 𝟏𝟎−𝟒 𝑻 diretto lungo asse y positivo


Capitolo 8

Es. 8.1

1. Ɛ𝒊 = −𝟏𝟒. 𝟒 𝑽

Es. 8.2

1. Ɛ𝒊 = −𝟎. 𝟎𝟖 𝑽

Es. 8.3

1. 𝑩 = 𝟎. 𝟒 ⋅ 𝟏𝟎−𝟒 𝑻


Capitolo 8

Es. 8.4

1. 𝑳 =𝝁𝟎𝑵

𝟐𝒂

𝟐 𝝅𝒍𝒏

𝑹+𝒃

𝑹

2. 𝑳𝒍 = 𝟏. 𝟐𝟔 ⋅ 𝟏𝟎−𝟓 𝑯/𝒎

• 𝑳𝒍,𝒌 = 𝟎. 𝟎𝟏𝟐𝟔 𝑯/𝒎

Es. 8.5

1. 𝑼𝒎 =𝝁𝟎𝑵

𝟐𝒂

𝟒 𝝅𝒍𝒏

𝑹+𝒃

𝑹𝒊𝟐 =

𝟏

𝟐𝑳 𝒊𝟐

Es. 8.6

1. 𝑴 = 𝝁𝟎𝒏𝟏𝑵𝟐𝚺𝟏


Capitolo 8

Es. 8.7

1. Ɛ𝒊 = 𝑴𝒊𝟎𝝎 𝒔𝒆𝒏𝝎𝒕, 𝑴 =𝝁𝟎𝑵𝟏𝑵𝟐𝝅𝒓𝟐

𝟐𝒄𝒐𝒔𝜽

𝟐𝒓𝟏

Es. 8.8

1. 𝑩 𝒓, 𝒕 =𝟏

𝟐𝝁𝟎𝜺𝟎𝝎𝑬𝟎𝒓 𝒄𝒐𝒔𝝎𝒕

2. Ɛ𝒊 =𝟏

𝟐𝚺′𝐍 𝝁𝟎𝜺𝟎𝝎

𝟐𝑬𝟎𝒓′𝒔𝒆𝒏𝝎𝒕 = 𝟎. 𝟎𝟏 𝒔𝒆𝒏𝟏𝟎𝟕𝒕 𝑽


Capitolo 8

Es. 8.9

1. 𝑭 = 𝟒 × 𝟏𝟎−𝟏𝟖 𝑵, diretta verso il basso

2. 𝚫𝐕 = 𝟏𝟖 𝐕, 𝐕 𝐏 > 𝐕 𝐐

Es. 8.10

1. 𝒊 = 𝟒 × 𝟏𝟎−𝟒 𝑨

Es. 8.11

1. 𝒂 = 𝟏𝟎 𝒄𝒎


Capitolo 8

Es. 8. 12

1. Ɛ𝒊 = 𝟖 × 𝟏𝟎−𝟖 𝑽 = 𝟖𝟎 𝒏𝑽

2. 𝐢 = 𝟖 × 𝟏𝟎−𝟗𝑨 = 𝟖 𝒏𝑨, verso orario

Es. 8.13

1. 𝒊 = 𝟎. 𝟑𝟐 𝑨, verso orario

Es. 8.14

1. 𝑩 𝒙 =𝝁𝟎𝑰

𝟐𝝅𝒙

2. 𝚽 𝑩 𝒙 =𝝁𝟎𝑰 𝒍

𝟐𝝅𝒍𝒏

𝒅 𝒕 +𝒍

𝒅 𝒕

3. 𝒊 = 𝟕 × 𝟏𝟎−𝟖 𝑨 = 𝟕𝟎 𝒏𝑨, verso orario


Capitolo 8

Es. 8. 15

1. 𝒉 𝒕 = 𝒗𝒕

2. 𝜱 𝑩(𝒕) = 𝑩𝟎𝒍𝟐 𝟏 +

𝒂

𝟐𝟐𝒗𝒕 + 𝒍

3. 𝒊 = −𝟔 × 𝟏𝟎−𝟓 𝑨, verso antiorario

Es. 8.16

1. 𝒕𝒎𝒂𝒙 = 𝟎. 𝟎𝟏 𝒔, Ɛ𝒊,𝒎𝒂𝒙 = 𝟕. 𝟖𝟓 𝑽

2. 𝑹 = 𝟒𝟎𝟎𝟎 𝜴, 𝒊𝒎𝒂𝒙 = 𝟏. 𝟗 𝒎𝑨


Capitolo 8

Es. 8. 17

1. Ɛ𝒊, = 𝟎. 𝟎𝟐 𝑽

2. 𝒊 = 𝟐𝒎𝑨, verso antiorario

3. Ɛ𝒊, = 𝟎

Es. 8.18

1. Ɛ𝒊, = −𝝁𝟎 𝒂 𝑰𝟎𝑵

𝟐 𝝅 𝝉𝒍𝒏

𝒉+𝒃

𝒉𝒆−𝒕/𝝉, 𝒊 = Ɛ𝒊, /𝑹, verso orario

2. 𝑬 = 𝟑. 𝟕 × 𝟏𝟎−𝟏𝟐 𝑱


Esercizi riepilogo

Es. R.1

1. 𝒊𝒂 = 𝟎. 𝟏𝟖 𝝁𝑨, 𝒊𝑩 = 𝟎

2. 𝚫𝚽 = 𝟎. 𝟏𝟔 𝝁𝑾𝒃

3. 𝒒 = 𝟏𝟔. 𝟐 𝒏𝑪

Es. R.2

1. 𝑩 = 𝟒. 𝟓 ⋅ 𝟏𝟎−𝟓 𝑻

Es. R.3

1. 𝒊𝒎𝒂𝒙 = 𝟒 𝑨

2. 𝑬𝒕𝒐𝒕 = 𝟏𝒎𝑱


Esercizi riepilogo

Es. R.4

1. 𝑩𝒉

𝟑= 𝟒. 𝟕 ⋅ 𝟏𝟎−𝟒 𝑻

2. 𝑩𝑫

𝟑= 𝟏. 𝟑 ⋅ 𝟏𝟎−𝟑 𝑻

3. 𝚽𝒍 = 𝟑𝟓 𝝁𝑾𝒃/𝒎

Es. R.5

1. 𝒗 = 𝟕. 𝟕 𝒎/𝒔

2. 𝑷 = 𝟎. 𝟕𝟔𝑾

Es. R.6

1. 𝒗 = 𝟎. 𝟑𝟑 𝒎𝑨


Esercizi riepilogo

Es. R.7

1. 𝑩𝑨 = −𝟓 ⋅ 𝟏𝟎−𝟓 𝑻

2. 𝑭𝒍 = 𝟎. 𝟏 𝑵/𝒎

3. 𝑹 = 𝟏. 𝟓 𝛀

4. 𝑸 = 𝟓. 𝟓 𝝁𝑪

Es. R.8

1. 𝒗 = 𝟎. 𝟒𝟖 𝒎/𝒔

2. 𝑭 = −𝟎. 𝟎𝟐𝟒 𝑵

3. 𝑸 = 𝟕𝟏. 𝟐 𝒎𝑪

4. 𝑾 = 𝟕. 𝟏 𝒎𝑱


Esercizi riepilogo

Es. R.9

1. 𝑭 = 𝟔𝒎𝑵

Es. R.10

1. 𝑳𝒍 =𝝁𝟎

𝟐 𝝅𝒍𝒏

𝑹𝟐

𝑹𝟏

𝑼𝒎,𝒍 =𝝁𝟎

𝟒 𝝅𝒍𝒏

𝑹𝟐

𝑹𝟏𝒊𝟐


soluzioni numeriche esercizi

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