Coulomb constant, k=8.987×109N⋅m2/C2. Vacuum permitivity, ϵ0=8.854×10−12F/m. Magnitude of the Charge of one electron, e=−1.60217662×10−19C. Mass of one electron, me=9.10938356×10−31kg. Mass of one proton, mp=1.6726219×10−27kg, Charge of one proton, ep=1.60217662×10−19C Unless specified otherwise, each symbol carries their usual meaning. For example, μC means microcoulomb . PartI Suppose, We have a dipole where 3 charges q1=3e,q2=2e,q3=−5e are placed on the vertices of the square as shown in the figure given above. Side length of the square is 3nm. a) Calculate the X and Y components of dipole moment of this dipole. b) Calculate the electric potential at point P due to this dipole. PartII Now suppose, we have a continuous charge distribution D for which potential at any point (x,y) in the xy plane is given by, V(x,y)=3xy(mx+n), where V is in volt, coordinates x, y are in meter, m, n both are constant and m=1N/Cm2, n=1N/Cm. c) Calculate the potential at point P due to continuous charge distribution D only. d) Calculate the total electric potential at point P and the potential energy of a proton if it is placed at point P? e) Calculate the x and y components of the electric field at point P. (Due to both dipole and continuous charge distribution D) f)i. Calculate the x and y components of the Coulomb force that is exerted on the proton placed at point P due to the net E field. ii. What will be the magnitude of acceleration that the proton will have due to this force?
Need help with parts (d), (e) and (f). Thank you.
Coulomb constant, k=8.987×109N⋅m2/C2. Vacuum permitivity, ϵ0=8.854×10−12F/m. Magnitude of the Charge of one electron, e=−1.60217662×10−19C. Mass of one electron, me=9.10938356×10−31kg. Mass of one proton, mp=1.6726219×10−27kg, Charge of one proton, ep=1.60217662×10−19C Unless specified otherwise, each symbol carries their usual meaning. For example, μC means microcoulomb .
PartI
Suppose, We have a dipole where 3 charges q1=3e,q2=2e,q3=−5e are placed on the vertices of the square as shown in the figure given above. Side length of the square is 3nm.
a) Calculate the X and Y components of dipole moment of this dipole.
b) Calculate the electric potential at point P due to this dipole.
PartII
Now suppose, we have a continuous charge distribution D for which potential at any point (x,y) in the xy plane is given by, V(x,y)=3xy(mx+n), where V is in volt, coordinates x, y are in meter, m, n both are constant and m=1N/Cm2, n=1N/Cm.
c) Calculate the potential at point P due to continuous charge distribution D only.
d) Calculate the total electric potential at point P and the potential energy of a proton if it is placed at point P?
e) Calculate the x and y components of the electric field at point P. (Due to both dipole and continuous charge distribution D)
f)i. Calculate the x and y components of the Coulomb force that is exerted on the proton placed at point P due to the net E field.
ii. What will be the magnitude of acceleration that the proton will have due to this force?
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