Find magnitude of the magnetic field

[define_normal]

Homework Statement

A wire carries a current of 30A along the x-axis from x = 0 to x = 3.0 cm. Determine the magnitude in uT of the magnetic field at the point y = 4.0 cm on the y-axis.

Homework Equations

dB = (u/4pi) ((Ids x r)/r^2)

The Attempt at a Solution

We tried using this formula, but it didn't work. We are lost. Please help! Be descriptive if you can.

 

[rl.bhat]

Homework Statement

A wire carries a current of 30A along the x-axis from x = 0 to x = 3.0 cm. Determine the magnitude in uT of the magnetic field at the point y = 4.0 cm on the y-axis.

Homework Equations

dB = (u/4pi) ((Ids x r)/r^2)

If you take a small element dx on x-axis at a distance x from the origin, its distance from a point on the y-axis is sqrt(x^2 + y^2)
Now (dx)xr = dx*sinθ, where r is the unit vector along r and θ is the angle between r and y-axis.
sinθ = x/sqrt(x^2 + y^2)
Substitute these values in dB and take the integration from x = 0 to x = 4

 

[define_normal]

We don't understand how we're supposed to integrate. Isn't there an R^2 in the bottom?

 

[rl.bhat]

We don't understand how we're supposed to integrate. Isn't there an R^2 in the bottom?

Yes. It is there.
B = μ_ο/4π*I*Intg[ sinθ*dx/( x^2 + y^2 )
If you substitute the value of sinθ,the expression becomes
B = μ_ο/4π*I*Intg[ x*dx/( x^2 + y^2 )^3/2
Now find the integration and substitute the limits.

 

[amdemare]

Can you write out what would be the exact (B=) equation?

 

[rl.bhat]

Can you write out what would be the exact (B=) equation?

B = - μo/4π*I/sqrt(x^2 + Y^2)