Calculating Magnetic Field in a Square with Varying Resistances

[arpon]

Homework Statement

[/B]
Consider a square whose successive sides of length $L$ has resistances $R, 2R, 2R, R$ respectively. If a potential difference $V$ is applied between the points (call them , say , A and B) where the sides with R and 2R meet. Find the magnetic field $B$ at the center of the square.

Homework Equations

$R_s = R_1 + R_2 + R_3 + ... + R_n$
$\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ... + \frac{1}{R_n}$
$V = iR$
$\oint \vec B \cdot d \vec s = \mu _0 i$

The Attempt at a Solution

The equivalent resistance of this combination is $\frac{4R}{3}$ . So, the current through $R , 2R$ are $\frac{V}{2R} , \frac{V}{4R}$ respectively. But, to calculate the magnetic field, what will be the amperian loop to imagine?

 

[TSny]

Does the magnetic field pattern have enough symmetry to use Ampere's law? If not, can you think of a different law that you can use?

 

[arpon]

So, I should use Biot-Savart's law. But another question, can I use Biot-Savart's Law in case of variable electric field?

 

[BvU]

No. There is a Maxwell[/PLAIN] correction involving dE/dt. (also this link)
But it's very small unless E changes very rapidly.

 

[TSny]

So, I should use Biot-Savart's law.

Yes.