1.8.21
Current-carrying wire basically ek nadī hai bhagte hue charges ki . Hum jaante hain ki ek akela moving
charge ek force feel karta hai F = q v × B trillions aise charges saath milke chal rahe hote hain — toh wire as a whole ek force feel karta hai.
WHY it matters: yahi principle hai har electric motor, loudspeaker, aur
moving-coil galvanometer ka. Electricity ko → motion mein convert karo.
Intuition HUM KYA KAR RAHE HAINHum F = B I L build karenge ek charge par force se, phir wire ki
length L
Setup. Ek seedhi wire lo jiska cross-sectional area A L I n q v d
Step 1 — Ek carrier par force.
F 1 = q v d × B Yeh step kyun? Yeh Lorentz force hai, ek matra magnetic force law jo humein chahiye.
Step 2 — Carriers count karo. Segment mein carriers ki sankhya:
N = n × ( volume ) = n A L Yeh step kyun? Total force = (force per carrier) × (kitne carriers hain).
Step 3 — Total force.
F = N F 1 = n A L ( q v d × B )
Step 4 — Current ko pehchano. Drift-current relation yaad karo:
I = n A q v d ⇒ n A q v d = I L L L conventional current direction ki taraf point karta hai.
Yeh step kyun? Isse hum microscopic cheezein ( n , A , q , v d ) I
Ek bent/curved wire ke liye hum infinitesimal pieces ko add karte hain:
d F = I d ℓ × B ⇒ F = I ∫ d ℓ × B
Uniform B F = I ( ∫ d ℓ ) × B ∫ d ℓ start se end tak straight vector hai. Toh ek curved wire wohi force feel karta hai jo uske endpoints ko join karne wali straight wire feel karti. Ek closed loop (∫ d ℓ = 0 zero net force feel karta hai (phir bhi torque feel kar sakta hai!).
Intuition Yahan LEFT hand kyun?Force hai F = I L × B F dono wire aur field ke perpendicular
hoti hai. Fleming's Left-Hand Rule bas isi cheez ka haath-gesture encoding hai.
Mnemonic Fleming's Left-Hand Rule (wire par force ke liye / motor)LEFT haath par thumb, First finger, seCond finger ko mutually perpendicular stretch karo:
F irst finger → F ield B seC ond finger → C urrent I
thuM b → M otion / Force F FBI ": Field–By first finger, current–seCond... force–thumb.)
Worked example Example 1 — straight wire, perpendicular fieldEk wire jis ki length 0.50 m I = 4.0 A B = 0.30 T
Solve. θ = 9 0 ∘ F = B I L = 0.30 × 4.0 × 0.50 = 0.60 N Yeh step kyun? Perpendicular ⇒ sin 9 0 ∘ = 1
Worked example Example 2 — wire at an angleSame wire lekin field se θ = 3 0 ∘
Solve. F = B I L sin θ = 0.30 × 4.0 × 0.50 × sin 3 0 ∘ = 0.60 × 0.5 = 0.30 N Yeh step kyun? Sirf wire ka B
Worked example Example 3 — left hand se directionCurrent east ki taraf flow kar rahi hai, field north ki taraf point karti hai (dono horizontal). Force kis taraf hai?
Solve. First finger north, second finger east → thumb upar (zameen se bahar) point karta hai.
Yeh step kyun? E ^ × x ^ = y ^ = z ^ = L × B ∝ x ^ × y ^ = z ^
Worked example Example 4 — semicircular wire (shortcut use karta hai)Ek semicircular wire jis ka radius R I B
Solve. Curved part par net force I L eff × B L eff 2 R F = I ( 2 R ) B Yeh step kyun? Uniform B F = I ( ∫ d ℓ ) × B ∫ d ℓ 2 R
Common mistake "Force field ke along hoti hai, jaiseB Kyun sahi lagta hai: gravity mein, force field g along hoti hai. Toh hum expect karte hain ki B Fix: magnetic force ek cross product hai — yeh dono I B B zero force milti hai, maximum nahi.
Common mistake "Ek closed current loop uniform field mein sideways dhakela jata hai."Kyun sahi lagta hai: loop ki har side clearly ek force feel karti hai. Fix: opposite sides par equal-and-opposite forces lagte hain, toh net force zero hoti hai (∮ d ℓ = 0 torque — yahi motor ko spin karta hai.
Common mistake Wire par force ke liye right hand use karna.Kyun sahi lagta hai: right-hand rule har jagah aata hai (jaise positive charge ke liye v × B Fix: Fleming's Left -Hand Rule motor rule hai. (Right-hand = generator
rule / v × B
sin θ Kyun sahi lagta hai: F = B I L Fix: woh sirf θ = 9 0 ∘ F = B I L sin θ
Recall Forecast-then-verify: aage padhne se pehle predict karo kiB sin 0 ∘ = 0 ⇒ F = 0 B v ∥ B ⇒ v × B = 0
Recall Feynman — ek 12-saal ke bache ko explain karoSocho ek bheed hai bache ki jo ek tezi se chalti hawa mein bhaag rahe hain. Hawa sirf bache ko sideways dhakeli hai jab woh hawa ke across bhaagta hai — agar tum seedha hawa mein bhaago, toh yeh khaas "magnetic wind" tumhe nahi dhakeli. Current wali wire mein bhagte hue electric charges ki bheed hoti hai. Charges ko magnetic field ke across line up karo aur poori wire sideways dhakeli jaati hai. Wire ko field ke along ghuma do aur koi nahi dhakela jaata. Yahi sideways dhakka motors ko spin karta hai.
Straight current wire par force (vector form)? B θ F = B I L sin θ
B Wire par force ki direction kis rule se milti hai? Fleming's Left-Hand Rule (F=Field=first finger, C=Current=second, M=Motion=thumb).
Uniform field mein closed current loop par net force?Zero (
∮ d ℓ = 0 ); lekin net torque ho sakta hai.
q v × B I L × B n A q v d = I L use karo aur force per carrier ko
N = n A L carriers se multiply karo.
Uniform B Same jaise ends ko join karne wali straight wire par:
F = I L eff × B .
0.5 4 0.3 F = B I L = 0.60
Lorentz force on a moving charge — parent law jisse humne yeh derive kiya.Drift velocity and current — I = n A q v d Torque on a current loop — loop ki net force zero hoti hai lekin torque motors chalata hai.Electric motor / Moving-coil galvanometer — direct applications.Force between two parallel currents — har wire doosri ke field mein baithi hai.Cross product (vectors) — perpendicularity ke peeche ki geometry.
generalise to curved wire
direction via cross product
Zero net force, may have torque
Motors, loudspeakers, galvanometers
