Question
Asked Dec 17, 2019
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An ionized oxygen molecule (o;) at point A has charge +e
and moves at 2.00 x 10 m/s in the positive x-direction. A
constant electric force in the negative x-direction slows the
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An ionized oxygen molecule (o;) at point A has charge +e and moves at 2.00 x 10 m/s in the positive x-direction. A constant electric force in the negative x-direction slows the

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molecule to a stop at point B, a distance of 0.750 mm past A
on the x-axis. Calculate (a) the x-component of the electric
field and (b) the potential difference between points A and B.
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molecule to a stop at point B, a distance of 0.750 mm past A on the x-axis. Calculate (a) the x-component of the electric field and (b) the potential difference between points A and B.

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Expert Answer

Step 1

According to the work done by the electric force will be the change in kinetic energy of the ionized oxygen molecule. This can be expressed as,

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w =mv}-?) Here, W is the work done by the electric force m is the mass of the molecule, v, is the final speed of the molecule and v, is the initial speed of the molecule. Since the molecule finally comes to rest, its final speed will be zero. Thus, -m(0-r;) 2 mv (1) The equation for the work done by the electric force is given by W = Fd cos e Here, F is the electric force, d is the distance through which the molecule is moved and 0 is the angle between the force and the displacement of the molecule. Since the molecule moves in +x direction and the force acts in -x direction, the value of e will be 180° . Thus, W = Fd cos180° = -Fd (2)

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Step 2

The electric force ...

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F = qE Here, q is the charge and E is the electric field. The charge of the ionized molecule is +e .Thus, F = eE Putting in equation (2), W = -eEd (3) Equating equations (1) and (3), -m; = -eEd - -- 2ed Substituting the numerical values, kg )(2.00 ×10° m/s) (5.31x10-6 2(1.60 x 10-19 C)(0.750×10³ m) = 885 V/m The electric force acts in the -x-direction, the electric field will also be directed along the -x direction. Thus, the x-component of the electric field is E, = -885 V/m .

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Electric Charges and Fields

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