    Question

# A particle of mass m and charge −q is projected from the origin with a horizontal speed v into a space having electric field of magnitude E directed downwards as shown in the figure. If the effect due to gravity can be neglected, then choose the correct statement(s) among the following. A
The equation of trajectory is y=12(qEx2mv2)
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B
The kinetic energy after a displacement y is qEy
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C
The horizontal and vertical displacements x and y after a time t are x=vt and y=12ayt2
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D
The horizontal and vertical components of acceleration are ax=0, ay=qEm
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Solution

## The correct option is D The horizontal and vertical components of acceleration are ax=0, ay=qEmSince, there is no force acting on the mass in the x direction, Fx=0 ∴ ax=0 Now, since the electric field acts downwards, the force acting on the particle in the y direction, Fy=qE ∴ Using Fy=may ay=qEm So, option (b) is the correct answer. Now considering the second equation of motion, x=uxt+12axt2 ∵ ux=v and ax=0 ⇒x=vt .....(1) Similarily, for y=uyt+12ayt2 ∵ uy=0 and ay=qEm y=12ayt2=12(qEm)t2 .....(2) So, option (d) is the correct answer. We, have from (1), t=xv Substituting t=xv in (2), we get y=12(qEx2mv2) So, option (c) is the correct answer. Now, kinetic energy KE is, KE=12m(v2x+v2y) where, vx=v and vy=ayt=qEmt KE=12m(v2+q2E2t2m2) So, option (a) is the incorrect answer. Hence, options (b) , (c) and (d) are the correct answers.  Suggest Corrections  0      Explore more