- #1

jisbon

- 476

- 30

- Homework Statement
- Derive an expression for the magnetic field at point P due to current-carrying wire of length a

- Relevant Equations
- NIL

So I think I do understand how to do this, but the thing is my answers are always incorrect. Will need some guidance/help on this.

##B =\frac{\mu_{0}I}{4\pi}\int\frac{dysin\theta}{r^2} ##

##y = Rtan\phi##

##dy = Rsec^2\phi d\phi##

##B = \frac{\mu_{0}I}{4\pi}\int\frac{dysin\theta}{r^2} = \frac{\mu_{0}I}{4\pi}\int\frac{Rsec^2\phi d\phi sin(\frac{\pi}{2}-\phi)}{R^2sec^2 \phi}

= \frac{\mu_{0}I}{4\pi}\int\frac{cos\phi}{R}d\phi = \frac{\mu_{0}I}{4\pi}(sin\phi_{2}-sin\phi_{1}) ##

So,

##sin\phi_{1}=\frac{2/3a}{\sqrt{4/9a^2+x^2}}##

##sin\phi_{2}=\frac{1/3a}{\sqrt{1/9a^2+x^2}} ##

##\frac{\mu_{0}I}{4\pi}(sin\phi_{2}-sin\phi_{1}) = \frac{\mu_{0}I}{4\pi} (\frac{1/3a}{\sqrt{1/9a^2+x^2}} - \frac{2/3a}{\sqrt{4/9a^2+x^2}})##

Is this correct?