# Homework Help: Calculation of magnetic field

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1. Dec 20, 2014

### arpon

1. The problem statement, all variables and given/known data

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.

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

3. 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?

2. Dec 20, 2014

### 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?

3. Dec 20, 2014

### 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?

4. Dec 20, 2014

### BvU

Last edited by a moderator: May 7, 2017
5. Dec 20, 2014

Yes.