Understanding the Zero Magnetic Field at the Center of a Square - Explained

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The magnetic field at the center of a square formed by four currents directed into the page is zero due to the cancellation of their effects. Each current generates a magnetic field that circulates clockwise, as determined by the right-hand rule. Specifically, the magnetic field contributions from opposite corners (1 with 3 and 2 with 4) negate each other. This results in no net magnetic field at the center of the square. The explanation confirms that the arrangement of the currents leads to complete cancellation.
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So I am trying to understand why the answer is zero for this problem.

Calculate the magnetic field at the center of the square.

The figure shows 4 circles with Xs (which I understand indicates, magnetic field direction is going into the page) forming into a square, if that makes any sense.

Please explain to me why the magnetic field is zero.
 
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Are the circles with X's in the corners possibly currents all going into the page?

Or are you saying that there are 4 flux lines at each corner going into the page?
 
LowlyPion said:
Are the circles with X's in the corners possibly currents all going into the page?

Or are you saying that there are 4 flux lines at each corner going into the page?

The circles with the Xs in the corners are currents all going into the page.
 
Well then what is the magnetic field about a current in a wire?

What is the B-field from each of the currents? And more importantly how are they directed?
 
LowlyPion said:
Well then what is the magnetic field about a current in a wire?

What is the B-field from each of the currents? And more importantly how are they directed?

Thanks someone explained it to me...

(x)1 (x)2

(x)3 (x)4

From RIGHT HAND RULE.
So the magnetic field on 1,2,3,4 are all clockwise. So 1 will be canceling out with 3 and 2 will be canceling out with 4. Therefore, there is no magnetic field.
 
Nimmy said:
Thanks someone explained it to me...

(x)1 (x)2




(x)3 (x)4

From RIGHT HAND RULE.
So the magnetic field on 1,2,3,4 are all clockwise. So 1 will be canceling out with 3 and 2 will be canceling out with 4. Therefore, there is no magnetic field.

There you go. You got it.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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