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Condition |
free/or 0.5$ |
| 701 | Two point charges, q and -q, are separated by a distance L, both being located at a distance L/2 from the infinite conducting plane. Find: (a) the modulus of the vector of the electric force acting on each charge; (b) the magnitude of the electric field strength vector at the midpoint between these charges. |
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| 702 | A point charge q is located between two mutually perpendicular conducting half-planes. Its distance from each half-plane is equal to l. Find the modulus of the vector of the force acting on the charge. |
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| 703 | A point dipole with an electric moment p is located at a distance l from an infinite conducting plane. Find the modulus of the vector of the force acting on the dipole if the vector p is perpendicular to the plane. |
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| 704 | A point charge q is located at a distance l from an infinite conducting plane. Determine the surface density of charges induced on the plane as a function of separation r from the base of the perpendicular drawn to the plane from the charge. |
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| 705 | A thin infinitely long thread carrying a charge λ per unit length is oriented parallel to the infinite conducting plane. The distance between the thread and the plane is equal to l. Find: (a) the modulus of the vector of the force acting on a unit length of the thread; (b) the distribution of surface charge density σ(x) over the plane, where x is the distance from the plane perpendicular to the conducting surface and passing through the thread. |
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| 706 | A very long straight thread is oriented at right angles to an infinite conducting plane; its end is separated from the plane by a distance l. The thread carries a uniform charge of linear density λ. Suppose the point O is the trace of the thread on the plane. Find the surface density of the induced charge on the plane (a) at the point O; (b) as a function of a distance r from the point O. |
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| 707 | A thin wire ring of radius R carries a charge q. The ring is oriented parallel to an infinite conducting plane and is separated by a distance l from it. Find: (a) the surface charge density at the point of the plane symmetrical with respect to the ring; (b) the strength and the potential of the electric field at the centre of the ring. |
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| 708 | Find the potential φ of an uncharged conducting sphere outside of which a point charge q is located at a distance l from the sphere's centre. |
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| 709 | A point charge q is located at a distance r from the centre O of an uncharged conducting spherical layer whose inside and outside radii are equal to R1 and R2 respectively. Find the potential at the point O if r < R1. |
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| 710 | A system consists of two concentric conducting spheres, with the inside sphere of radius a carrying a positive charge q1. What charge q5 has to be deposited on the outside sphere of radius b to reduce the potential of the inside sphere to zero? How does the potential cp depend in this case on a distance r from the centre of the system? Draw the approximate plot of this dependence. |
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| 711 | Four large metal plates are located at a small distance d from one another as shown in Fig. 3.8. The extreme plates are interconnected by means of a conductor while a potential difference Δφ is applied to internal plates. Find: (a) the values of the electric field strength between neighbouring plates; (b) the total charge per unit area of each plate. |
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| 712 | Two infinite conducting plates 1 and 2 are separated by a distance L. A point charge q is located between the plates at a distance x from plate 1. Find the charges induced on each plate. |
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| 713 | Find the electric force experienced by a charge reduced to a unit area of an arbitrary conductor if the surface density of the charge equals σ. |
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| 714 | A metal ball of radius R = 1.5 cm has a charge q = 10 μC. Find the modulus of the vector of the resultant force acting on a charge located on one half of the ball. |
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| 715 | When an uncharged conducting ball of radius R is placed in an external uniform electric field, a surface charge density s = s0cosT is induced on the ball's surface (here ao is a constant, is a polar angle). Find the magnitude of the resultant electric force acting on an induced charge of the same sign. |
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| 716 | An electric field of strength E = 1.0 kV/cm produces polarization in water equivalent to the correct orientation of only one out of N molecules. Find N. The electric moment of a water molecule equals p = 0.62·10^(-29) C•m. |
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| 717 | A non-polar molecule with polarizability β is located at a great distance l from a polar molecule with electric moment p. Find the magnitude of the interaction force between the molecules if the vector p is oriented along a straight line passing through both molecules. |
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| 718 | A non-polar molecule is located at the axis of a thin uniformly charged ring of radius R. At what distance x from the ring's centre is the magnitude of the force F acting on the given molecule (a) equal to zero; (b) maximum? Draw the approximate plot Fx(x). |
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| 719 | A point charge q is located at the centre of a ball made of uniform isotropic dielectric with permittivity ε. Find the polarization P as a function of the radius vector r relative to the centre of the system, as well as the charge q' inside a sphere whose radius is less than the radius of the ball. |
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| 720 | Demonstrate that at a dielectric-conductor interface the surface density of the dielectric's bound charge σ' = -σ(ε - 1)/ε, where ε is the permittivity, σ is the surface density of the charge on the conductor. |
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