text: Tamil Nadu Board of Secondary EducationHSC Science Class 12th
  
  # Derive the expression for the force between two parallel, current-carrying conductors. - Physics
  
  Numerical
  
  Derive the expression for the force between two parallel, current-carrying conductors.
  
  #### Solution
  
  1. Two long parallel current-carrying conductors separated by a distance V in air.
  2. I1, I2 – current passing through the conductors A and B in the same direction.
  3. Magnetic field due to current I2 of elemental length dl in A
  vec"B"_1 = (mu_0"I"_1)/(2pi"r") (- hat"i")
  vec"B"_1 = (- mu_0"I"_1)/(2pi"r") hat"i"
  4. The direction of magnetic field is perpendicular to the plane of the paper and outwards.
  5. A force on a small elemental length dl in B, experience magnetic field B1.
  
  "d"vec"F" = ("I"_2 vec"d"l xx vec"B"_1)
  
  = - "I"_2"dl" (mu_0 "I"_1)/(2pi"r") (hat"k" xx hat"i")
  
  "d"vec"F" = (- mu_0 "I"_1"I"_2"dl")/(2pi"r")
  
  Force per unit length of the conductor.
  
  vec"F"/l = (- mu_0"I"_1"I"_2)/(2pi"r") hat"j"
  
  Magnetic field due to current I2 of elemental
  
  length dl in A
  
  vec"B"_2 = (mu_0"I"_2)/(2pi"r") hat"i"
  
  The direction of a magnetic field is perpendicular to the plane of the paper and outwards.
  
  Force on conductor A is directed towards conductor B.
  
  dF = ("I"_1 "d" vec"l" xx vec"B"_2)
  
  = "I"_1"dl" (mu_0 "I"_2)/(2pi"r") (hat"k" xx hat"i")
  
  "d"vec"F" = (mu_0 "I"_1"I"_2 "dl")/(2pi"r") hat"j"
  
  Force per unit length of the conductor A,
  
  vec"F"/l = (- mu"I"_1"I"_2)/(2pi"r") hat"j"
  
  Attractive force – direction of electric current is same.
  
  Repulsive force – direction of electric current is opposite.
  
  Concept: Lorentz Force
  Is there an error in this question or solution?
  
  #### APPEARS IN
  
  Tamil Nadu Board Samacheer Kalvi Class 12th Physics Volume 1 and 2 Answers Guide
  Chapter 3 Magnetism and magnetic effects of electric current
  Evaluation | Q III. 13. | Page 192
  Share
metadata: {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}