# 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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