The electric potential varies in space according to the relation $$V=3x+4y$$. A particle of mass $$0.1$$ kg starts from rest from point (2$$,$$3.2) under the influence of this field. The charge on the particle is $$+1$$ μC. Assume V and (x$$, $$y) are in SI units.The component of electric field in the $$x-direction$$ (Ex) isThe component of electric field in the $$y-direction$$ (Ey) isThe time taken to cross the $$x-axis$$ isThe velocity of the particle when it crosses the $$x-axis$$ is

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The electric potential varies in space according to the relation $$V=3x+4y$$. A particle of mass $$0.1$$ kg starts from rest from point (2$$,$$3.2) under the influence of this field. The charge on the particle is $$+1$$  μC. Assume V and (x$$, $$y) are in SI units.The component of electric field in the $$x-direction$$ (Ex) isThe component of electric field in the $$y-direction$$ (Ey) isThe time taken to cross the $$x-axis$$ isThe velocity of the particle when it crosses the $$x-axis$$ is

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$$Ex=$$−δVδ$$x=$$−$$3$$  Vm−$$1$$;  $$Ey=$$−δVδ$$y=$$−$$4$$  Vm−$$1ax=qExm=$$−$$1$$×$$10$$−$$6$$×$$30.1=$$−$$3$$×$$10$$−$$5$$  ms−$$2ay=qEym=$$−$$1$$×$$10$$−$$6$$×$$40.1=$$−$$4$$×$$10$$−$$5$$  ms−$$2Time$$ taken to cross the $$x-axisUsing$$ $$s=ut+12at2$$  we  $$get3.2=12$$×$$4$$×$$10$$−$$5$$  $$t2or$$ $$t=400$$  $$svx=axt=$$−$$3$$×$$10$$−$$5$$×$$400=12$$×$$10$$−$$3$$  ms−$$1vy=ayt=$$−$$4$$×$$10$$−$$5$$×$$400=16$$×$$10$$−$$3$$  ms−$$1v=vx2+vy2=20$$×$$10$$−$$3$$  ms−$$1Ex=$$−δVδ$$x=$$−$$3$$  Vm−$$1$$;  $$Ey=$$−δVδ$$y=$$−$$4$$  Vm−$$1ax=qExm=$$−$$1$$×$$10$$−$$6$$×$$30.1=$$−$$3$$×$$10$$−$$5$$  ms−$$2ay=qEym=$$−$$1$$×$$10$$−$$6$$×$$40.1=$$−$$4$$×$$10$$−$$5$$  ms−$$2Time$$ taken to cross the $$x-axisUsing$$ $$s=ut+12at2$$  we  $$get3.2=12$$×$$4$$×$$10$$−$$5$$  $$t2or$$ $$t=400$$  $$svx=axt=$$−$$3$$×$$10$$−$$5$$×$$400=12$$×$$10$$−$$3$$  ms−$$1vy=ayt=$$−$$4$$×$$10$$−$$5$$×$$400=16$$×$$10$$−$$3$$  ms−$$1v=vx2+vy2=20$$×$$10$$−$$3$$  ms−$$1Ex=$$−δVδ$$x=$$−$$3$$  Vm−$$1$$;  $$Ey=$$−δVδ$$y=$$−$$4$$  Vm−$$1ax=qExm=$$−$$1$$×$$10$$−$$6$$×$$30.1=$$−$$3$$×$$10$$−$$5$$  ms−$$2ay=qEym=$$−$$1$$×$$10$$−$$6$$×$$40.1=$$−$$4$$×$$10$$−$$5$$  ms−$$2Time$$ taken to cross the $$x-axisUsing$$ $$s=ut+12at2$$  we  $$get3.2=12$$×$$4$$×$$10$$−$$5$$  $$t2or$$ $$t=400$$  $$svx=axt=$$−$$3$$×$$10$$−$$5$$×$$400=12$$×$$10$$−$$3$$  ms−$$1vy=ayt=$$−$$4$$×$$10$$−$$5$$×$$400=16$$×$$10$$−$$3$$  ms−$$1v=vx2+vy2=20$$×$$10$$−$$3$$  ms−$$1Ex=$$−δVδ$$x=$$−$$3$$  Vm−$$1$$;  $$Ey=$$−δVδ$$y=$$−$$4$$  Vm−$$1ax=qExm=$$−$$1$$×$$10$$−$$6$$×$$30.1=$$−$$3$$×$$10$$−$$5$$  ms−$$2ay=qEym=$$−$$1$$×$$10$$−$$6$$×$$40.1=$$−$$4$$×$$10$$−$$5$$  ms−$$2Time$$ taken to cross the $$x-axisUsing$$ $$s=ut+12at2$$  we  $$get3.2=12$$×$$4$$×$$10$$−$$5$$  $$t2or$$ $$t=400$$  $$svx=axt=$$−$$3$$×$$10$$−$$5$$×$$400=12$$×$$10$$−$$3$$  ms−$$1vy=ayt=$$−$$4$$×$$10$$−$$5$$×$$400=16$$×$$10$$−$$3$$  ms−$$1v=vx2+vy2=20$$×$$10$$−$$3$$  ms−$$1$$

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The electric potential varies in space according to the relation $V = 3 x + 4 y .$ A particle of mass 0.1 kg starts from rest from point (2,3.2) under the influence of this field. The charge on the particle is $+ 1 μ C .$ Assume V and (x, y) are in SI units.

The component of electric field in the x-direction $(E_{x})$ is

The component of electric field in the y-direction $(E_{y})$ is

The time taken to cross the x-axis is

The velocity of the particle when it crosses the x-axis is

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