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A thin wire, carrying a positive and uniform linear charge density 2, is bent into a quarter-circle with a radius R, as shown in the figure. (a) Derive the electric potential at the center of the circle. (b) USE the result in part (a), calculate the electric field at the center. (c) If the line is not thin, but has a finite width w (as shown in the second diagram), what would the electric potential at the center be? (d) Derive the electric field

A thin wire, carrying a positive and uniform linear charge density 2, is bent into a quarter-circle with a radius R, as shown in the figure. (a) Derive the electric potential at the center of the circle. (b) USE the result in part (a), calculate the electric field at the center. (c) If the line is not thin, but has a finite width w (as shown in the second diagram), what would the electric potential at the center be? (d) Derive the electric field

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Bartley expert give me wrong solution plz solve this problem correctly all parts will definitely upvote and give positive feedback 

A thin wire, carrying a positive and uniform linear charge density 2, is bent into a quarter-circle with a radius R, as shown in the figure. (a) Derive the electric potential at the center of the circle. (b) USE the result in part (a), calculate the electric field at the center. (c) If the line is not thin, but has a finite width w (as shown in the second diagram), what would the electric potential at the center be? (d) Derive the electric field of this thick quarter-circle at the center, assuming the charge density is still uniform. (9) We have given a quarter circle with radius R having uniform linear charge density Lamda. charge Density = λ 20 4 (STR) TIR dq=1dx dg= 22dx TIR 211R dv=f_kd₂ R av = kg = √2/² TIR v= [av = 1/2 (²02) 50 R V= v= √dv=2k [x] 27² 4 2KQ AR₂ V= KB V= K R2 R² x 24 £= X V= KA 2R 2TIR AR 4.dx Electorc freeld £=-V dR K 2R2 R R Q = AⓇ KA(-1) 2R2
Transcribed Image Text:A thin wire, carrying a positive and uniform linear charge density 2, is bent into a quarter-circle with a radius R, as shown in the figure. (a) Derive the electric potential at the center of the circle. (b) USE the result in part (a), calculate the electric field at the center. (c) If the line is not thin, but has a finite width w (as shown in the second diagram), what would the electric potential at the center be? (d) Derive the electric field of this thick quarter-circle at the center, assuming the charge density is still uniform. (9) We have given a quarter circle with radius R having uniform linear charge density Lamda. charge Density = λ 20 4 (STR) TIR dq=1dx dg= 22dx TIR 211R dv=f_kd₂ R av = kg = √2/² TIR v= [av = 1/2 (²02) 50 R V= v= √dv=2k [x] 27² 4 2KQ AR₂ V= KB V= K R2 R² x 24 £= X V= KA 2R 2TIR AR 4.dx Electorc freeld £=-V dR K 2R2 R R Q = AⓇ KA(-1) 2R2
Step 2 If it is not line while finite width then (e) charge Density. TIR-TE2 6= -1 (1-1) dq=&ds V= = √d v= √k³2= K √α2= K fods (8) |V= V=Kods V=-R55 (TIR²_TIW2) } 4 Ebctoic field E = T ko 6 S TI KG (R2- w2 4 R V- ゴの R 4-R2 (R²_W²) R
Transcribed Image Text:Step 2 If it is not line while finite width then (e) charge Density. TIR-TE2 6= -1 (1-1) dq=&ds V= = √d v= √k³2= K √α2= K fods (8) |V= V=Kods V=-R55 (TIR²_TIW2) } 4 Ebctoic field E = T ko 6 S TI KG (R2- w2 4 R V- ゴの R 4-R2 (R²_W²) R
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