91Ó°ÊÓ

Three nested hollow spheres have the same centre. The innermost sphere has the radius of 2 cmand carries a uniformly distributed charge of $\mathbf{6}\mathbf{ }\mathbf{nC}\mathbf{(}\mathbf{1}\mathbf{ }\mathbf{nC}\mathbf{=}\mathbf{1}\mathbf{×}{\mathbf{10}}^{\mathbf{-}\mathbf{9}}\mathbf{ }\mathbf{C}\mathbf{)}$. The middle sphere has a radius of5 cm and carries a uniformly distributed charge of $\mathbf{-}\mathbf{4}\mathbf{ }\mathbf{nC}$. The outermost sphere has a radius of 10 cm and carries a uniformly distributed charge of $\mathbf{}\mathbf{8}\mathbf{ }\mathbf{nC}$.(a) What is the magnitude of the electric field at a distance of 1 cmfrom the centre? (b)What is the magnitude of the electric field at a distance of 4 cmfrom the centre?(c) What is the magnitude of the electric field at a distance of 9 cmfrom the centre?

A dipole is located at the origin and is composed of charged particle with charge $\mathbf{+}\mathbf{e}$and $\mathbf{-}\mathbf{e}$, separated by a distance $\mathbf{6}\mathbf{×}{\mathbf{10}}^{\mathbf{−}\mathbf{10}}\mathbf{\text{″¾}}$along the $\mathbf{x}$axis. The charge $\mathbf{+}\mathbf{e}$is on the $\mathbf{+}\mathbf{x}$axis. Calculate the electric field due to this dipole at a location $\mathbf{(}\mathbf{0}\mathbf{,}\mathbf{−}\mathbf{5}\mathbf{×}{\mathbf{10}}^{\mathbf{−}\mathbf{8}}\mathbf{,}\mathbf{0}\mathbf{)}\mathbf{\text{″¾}}$ .

A dipole is located at the origin and is composed of charged particles with charge$\mathbf{+}\mathit{e}\mathbf{}\mathit{a}\mathit{n}\mathit{d}\mathbf{-}\mathit{e}$, separated by a distance $\mathbf{2}\mathbf{×}{\mathbf{10}}^{\mathbf{-}\mathbf{10}}\mathbf{}\mathbf{\text{m}}$along the x axis. Calculate the magnitude of electric field due to this dipole at a location$\left(0,3×{10}^{-8},0\right)\mathbf{}\mathit{m}\mathbf{.}$

The dipole moment of the HF (hydrogen fluoride) molecule has been measured to $\mathbf{6}\mathbf{.}\mathbf{3}\mathbf{×}{\mathbf{10}}^{\mathbf{-}\mathbf{30}\mathbf{}}\mathbf{C}\mathbf{â‹\dots }\mathbf{m}\mathbf{.}$. If we model the dipole as having charges of +eand -e separated by a distance s, what is s ? Is this plausible?

A dipole is located at the origin and is composed of charged particles with charge $\mathbf{+}\mathbf{e}$and$\mathbf{-}\mathbf{e}$ , separated by a distance$\mathbf{6}\mathbf{×}{\mathbf{10}}^{\mathbf{-}\mathbf{6}}\mathbf{ }\mathbf{m}$ along the y axis. The $\mathbf{+}\mathbf{e}$charge on -y axis. Calculate the force on a proton due to this dipole at a location$\mathbf{(}\mathbf{0}\mathbf{,}\mathbf{4}\mathbf{×}{\mathbf{10}}^{\mathbf{-}\mathbf{8}}\mathbf{,}\mathbf{0}\mathbf{)}\mathbf{ }\mathbf{m}$ .

A dipole is located at the origin and is composed of charged particles with charge $\mathbf{+}\mathbf{2}\mathbf{e}\mathbf{}\mathbf{and}\mathbf{}\mathbf{-}\mathbf{2}\mathbf{e}$, separated by a distance $\mathbf{2}\mathbf{×}{\mathbf{10}}^{\mathbf{-}\mathbf{10}}\mathbf{m}$along the y axis. The $\mathbf{+}\mathbf{2}\mathbf{e}$charge is on the $+\mathrm{y}$axis. Calculate the force on a proton at a location $\left(0,0,3Â\pm {10}^{-8}\right)\mathbf{m}$due to this dipole.

A dipole consists of two charges $+\mathbf{6}\text{ }\mathbf{nC}$and $−\mathbf{6}\text{ }\mathbf{nC}$, held apart by a rod of length $\mathbf{3}\text{ }\mathbf{mm}$, as shown in Figure 13.71. (a) What is the magnitude of the electric field due to the dipole at location A, $\mathbf{5}\text{ }\mathbf{cm}$from the center of the dipole? (b) What is the magnitude of the electric field due to the dipole at location B, $\mathbf{5}\text{ }\mathbf{cm}$from the center of the dipole?

A dipole is centered at the origin and is composed of charged particles with charge +2e and -2e, separated by a distance $\mathbf{7}\mathbf{×}{\mathbf{10}}^{\mathbf{-}\mathbf{10}}\mathbf{m}$along the y axis. The +2e charge is on the -y axis, and the -2echarge is on the +y axis. (a) A proton is located at$<0,3×{10}^{-8},0>\mathbf{m}$. What is the force on the proton due to the dipole? (b) An electron is located at$<-3×{10}^{-8},0,0>\mathbf{m}$. What is the force on the electron due to the dipole? (Hint: Make a diagram. One approach is to calculate magnitudes, and get directions from your diagram.)

Two dipoles are oriented as shown in Figure 13.72. Each dipole consists of two charges +qand -q, held apart by a rod of length s, and the center of each dipole is a distance dfrom location A. If$\mathbf{=}\mathbf{2}\mathbf{nC}$, $\mathbf{s}\mathbf{=}\mathbf{1}\mathbf{mm}$and d=8cm, what is the electric field at location A? (Hint: Draw a diagram and show the direction of each dipole’s contribution to the electric field on the diagram.)

A dipole is located at the origin, and is composed of charged particles with charge +e and -e, separated by a distance 2x10^-10 along the axis. (a) Calculate the magnitude of the electric field due to this dipole at location $<0,2×{10}^{-8},0>\mathit{m}$. (b) Calculate the magnitude of the electric field due to this dipole at location $<2×{10}^{-8},0,0>\mathit{m}$.