Question

An electron is chasing a proton up the page. What happens to their paths if a magnetic field is suddenly turned on perpendicular to the surface of the page.

16. The drawing shows four situations in which two very long wires are carrying the same current, although the directions of the currents may be different. The point \(P\) in the drawings is equidistant from each wire. Which one (or more) of these situations gives rise to a zero net magnetic field at P ? 

\(\begin{array}{lllll} \text { (a) } 2 \text { and } 4 & \text { (b) Only } 1 & \text { (c) Only } 2 & \text { (d) } 2 \text { and } 3\end{array}\)

(e) 3 and 4

Answer 1

Direction of magnetic field at a point due to current carrying wire is determined by right hand rule.

If thumb of right hand is in direction of current then, perpendicular to the palm is the direction of magnetic field at that point.

Since point P is equidistant from all the wires, so magnitude of magnetic field is equal for all the wires.

Now we observe that in figure 1 and 3, magnetic fields are in same direction, so net magnetic field is not zero.

But in figure 2 and 4, direction are opposite and magnitude is equal. So they cancel out each other. So net magnetic field is zero.

Answer 2

Solution:

The magnetic field is zero in figures (2) and( 4 ).

If we apply the Right Hand thumb Rule,for figures \((1)\) and \((3)\) :

Due to the lower wire, by using the RightHand Rule it is clear that \(\mathrm{B}\) into the screen. Due to the upper wire, al so get a magnetic field into the screen. Which means that the net magnetic field will be twice the same one in the samedirection that will be into the screen. The same thing happens for figure 3 al so if we use Right Hand thumb Rule.

But if we apply the Right Hand thumb Rule, for figures \((2)\) and \((4):\)

due to the lower wire, the \(\mathrm{B}\) is out of the screen,

while due to the upper wire it is into the screen.Since the currents are same for both wires and the distance is al so the same, but in opposite direction. Thus they will cancel each other.