First Electric then Magnetic!

A particle having charge \(1 \text{ C}\) and mass of \(1 \text{ kg}\) is released from rest at origin. There are electric and magnetic fields given by

\(\displaystyle \vec{E} = (10 \hat{i})N/C \quad \text{for} \quad x \leq 1.8 \text{ m}\)

\(\displaystyle \vec{B} = (-5 \hat{k})T \quad \text{for} \quad 1.8 \text{ m} \leq x \leq 2.4 \text{ m}\)

A screen is placed parallel to \(\text y \)-\(\text z\) plane at \(x = 3 \text{ m}\). The y-coordinate of particle where it collides with the screen can be written as

\[ \dfrac{a(b - \sqrt{c})}{d}\]

Where \(\text{gcd}(a,d) = 1\) and c is square free. Find \(a+b+c+d\).

Details and Assumptions:

  • Neglect gravity.

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