Electric Charges And Fields

Q: In a certain region of space, electric field is along the z-direction throughout. The magnitude of electric field is however not constant, but increases uniformly along the positive z-direction at the rate of \$10^{5}N\ C^{-1}m^{-1}\$. The force experienced by the system having a total dipole moment equal to \$10^{-7}C\ m\$ in the negative \$z-direction\$ is

Consider an electric dipole with \$-q\$ charge at \$A\$ and \$+q\$ charge at \$B\$, placed along z-axis, such that its dipole moment is in negative \$z\$ direction.i.e., \$P_{z} = 10^{-7}C\ m\$The electric field is along positive direction of z-axis, such that\$\dfrac {dE}{dz} = 10^{5} N\ C^{-1} m^{-1}\$From, \$F = qdE\$\$= (q\times dz) \times \dfrac {dE}{dz} = p \dfrac {dE}{dz}\$Force experienced by the system in the negative z-direction,\$F = p\times \left (-\dfrac {dE}{dz}\right ) = 10^{-7} \times (-10^{5}) = -10^{-2}N\$.

Q: Gauss's law can't be used to calculate electric field near an electric dipole.

Electric dipole don't have symmetrical charge distribution.

Q: Electric field outside a long wire carrying charge q is proportional to :

Using Gauss Law across the cylindrical Gaussian surface,\$\displaystyle\int E.dS = \dfrac{q_{enc}}{\epsilon_0}\$\$\therefore E\times 2\pi r \times l = \dfrac{\lambda\times l}{\epsilon_0}\$\$\therefore E = \dfrac{\lambda}{2\pi r\epsilon_0}\$Here \$\lambda\$ is the linear charge density on the wire.

Question

In a certain region of space, electric field is along the z-direction throughout. The magnitude of electric field is however not constant, but increases uniformly along the positive z-direction at the rate of $1 0^{5} N C^{- 1} m^{- 1}$ . The force experienced by the system having a total dipole moment equal to $1 0^{- 7} C m$ in the negative $z - d i r e c t i o n$ is

Electric Charges And Fields

Physics 3172 Views

Gauss's law can't be used to calculate electric field near an electric dipole.

Electric dipole don't have symmetrical charge distribution.

Electric field outside a long wire carrying charge q is proportional to :

Physics
3172 Views