Two parallel beams of protons and electrons,c | vedclass

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(C) Let the proton beam be at $x = 0$ and the electron beam be at $x = d$. The current $I$ in both beams is equal in magnitude. For a point $P$ at dis

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(C) Let the proton beam be at $x = 0$ and the electron beam be at $x = d$. The current $I$ in both beams is equal in magnitude. For a point $P$ at distance $x$ from the proton beam,the magnetic field due to the proton beam is $B_p = \frac{\mu_0 I}{2 \pi x}$ (directed inwards,$\otimes$). The magnetic field due to the electron beam at distance $(d - x)$ is $B_e = \frac{\mu_0 I}{2 \pi (d - x)}$ (also directed inwards,$\otimes$,because the electron current is in the opposite direction). The net magnetic field is $B = B_p + B_e = \frac{\mu_0 I}{2 \pi} \left( \frac{1}{x} + \frac{1}{d - x} ight)$. As $x 	o 0$,$B 	o \infty$. As $x 	o d$,$B 	o \infty$. At $x = d/2$,$B$ is minimum. This corresponds to a $U$-shaped curve where $B$ is positive and approaches infinity at both boundaries $x=0$ and $x=d$. Among the given options,graph $(c)$ represents this behavior.

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