Question

A charged particle of mass 2 kg and charge 2 micro coulomb is proiected at an angle theta = 45 with the ground with the speed 20 metre per second. A horizontal electric field of 2 x 107 volt

Answer 1

your question is incomplete. A complete question is ------> A charged particle of mass m=2kg and charge q=2μC is thrown from a horizontal ground at an angle θ=45° with speed 20m/s. In space a horizontal electric field E = 2 × 10^7 V/m exist Find the range on horizontal ground of the projectile.

solution : trajectory of motion must be a parabolic but along x axis motion of particle also will be accelerated.

first of all, find time of flight ,

T = 2usin∅/g

here, u = 20m/s, ∅ = 45°

so, T = 2 × 20 sin45°/10 = 2√2 sec

[ note : time of flight doesn't change because it is found by using vertical component. I mean, y = $u_y T-\frac{1}{2}gT^2=0$]

Using formula, $F=qE=ma_x$

or, $a_x=\frac{qE}{m}$

= 2 × 10^-6 × 2 × 10^7/2

= 20 m/s²

now, Range , x = $u_xT+\frac{1}{2}a_xT^2$

= 20cos45° × 2√2 + 1/2 × 20 × (2√2)²

= 20 × 1/√2 × 2√2 + 10 × 8

= 40 + 80

= 120 m

hence, range = 120m