Please help with answering all questions. THank you electron orbiting it The Boh

Question

Please help with answering all questions. THank you

electron orbiting it The Bohr model of the hydrogen atom has a the the us and an in a with radius of 5.29 What is the work done by field on the electron's orbit? Work done a. 8.74 x 10 J b 8.74 x 10 J C. O J Extra-credit #2 particle, au is tied by a string to the ceiling and allowed to hang. A uniform A charged making the particle swing to electric field runs horizontally (left to right) through this region charged particle of equal the right at an from the vertical replaced by a new What can be said mass, Q2, it is angle from the vertical. observed that the angle is now to the left at 25 about the charged particles? a Q1 has more charge and is the same sign to Q2 b. Q1 has less charge and is opposite in sign to Q2 c. Qi has less charge and is the same sign to Q2 d. Qi has more charge and is opposite in sign to Q2 Extra Credit #3 110pts.: A 2 uF capacitor originally has no dielectric and is connected to a 10V battery. After being disconnected, the capacitor is filled with a dielectric with a value of 4.Q.What is the value of a (possibly) new battery that needs to be connected in order to store the same amount arge as before? a. 2.5 V 5 V c 10 V d, 0.4 V Proceed to the Written Problems.

Explanation / Answer

Q1.

the electric force is radially inward and the angle between force and the direction of motion is always perpendicular.

as work done=force*displacement*cos(angle)

and cos(90)=0

total work done is zero.

so option c is correct.

Q2. let tension in the string be T, mass of the charge be m and charge be q.

angle with vertical be theta and electric field magnitude is E.

balancing forces in horizontal direction:

T*sin(theta)=q*E...(1)

balancing forces in vertical direction:

T*cos(theta)=m*g...(2)

where m remains the same and theta increases, cos(theta) decreases

and hence T=m*g/cos(theta) increases.

from equation 1, T is increasing and sin(theta) is increasing

so q will be higher than its previous value.

hence Q2 > Q1

as the charge moves in opposite direction to the direction of field, then sign of charge Q2 is different to Q1.

so option b is correct.

Q3. charge on capacitor after being disconnected=2 uF*10 V=20 uC

when capacitor is filled with dielectric, new capacitance value=dielectric constant*original capacitance

=4*2 uF=8 uF

voltage value=charge/capacitance

=20 uC/8 uF=2.5 V

so otpion a is correct.

Q4. area=0.023^2=5.29*10^(-4) m^2

charge=3.6*10^(-11) C

if sepration is d, then capacitance=epsilon*area/d

=8.85*10^(-12)*5.29*10^(-4)/d

=4.68165*10^(-15)/d

then potential difference=charge/capacitance

=7689.596*d volts

for the positron:

change in potential energy=increase in kinetic energy

==>charge*potential difference=0.5*mass*speed^2

==>1.6*10^(-19)*7689.596*d=0.5*9.1*10^(-31)*(2*10^6)^2

==>d=1.48*10^(-3) m

hence option c is correct.

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