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physics
electricity and magnetism

Questions and Answers of Electricity and Magnetism

A proton and electron have the same kinetic energy upon entering a region of constant magnetic field. What is the ratio of the radii of their circular paths?
The power cable for an electric trolley (Fig 20-64) carries a horizontal current 0f 330 A toward the east. The Earth€™s magnetic field has a strength 5.0 X 10-5 T and makes an angle of dip
Calculate the force on an airplane which has acquired a net charge of 1550uC and moves with a speed of 120m/s perpendicular to the Earth’s magnetic field of 5.0 X 10-5 T.
Near the equator, the Earth’s magnetic field points almost horizontally to the north and has magnitude B = 0.50 X 10-4 T. What should be the magnetic and direction for the velocity of an electron
A doubly charged helium atom, who mass is 6.6 X 10-27 Kg is accelerated by a voltage of 2400V.(a) What will be its radius of curvature in a uniform 0.240-T field?(b) What is its period of revolution?
A sort of €˜€™projectile launcher€™€™ is shown in Fig. 20-65. A large current moves in a closed loop composed of fixed rails, a power supply, and a very light,
In Fig. 20-60 the top wire is 1.00-mm-distance copper wire and is suspended in air due to the two magnetic force from the bottom two wires The current flow through the two bottom wires is 95 A in
Two stiff parallel wires a distance l apart in a horizontal plane act as rails to support a light metal rod of mass m (perpendicular to each rail), Fig 20-66, A magnetic field B, directed vertically
Estimate the approximate maximum defection of the electron beam near the center of a TV screen due to the Earth’s 5.0 X 10-5 T field. Assume the CRT screen (section 17-10) is 22cm from the electron
(c) If the radius of the cyclotron is 2.0m and the magnetic field strength is 0.50T, what will be the maximum kinetic energy of accelerated protons in MeV
Four very straight parallel wires, located at the corners of a square of side l, carry equal currents l0 perpendicular to the page as shown in Fig. 20-68, Determine the magnitude and direction of B
Magnetic fields are very useful in particle accelerators for €˜€™beam steering€™€™: that is, the magnetic field can be used to changes the beam€™s
The magnetic field B at the center of a circular coil of wire carrying a current l (as in Fig, 20-9) isWhere N is the number of loops in the coil and r is its radius. Suppose that an electromagnet
Near the Earth’s poles the magnetic field is about 1 G (1 X 10-4T). Imagine a simple model in which the Earth’s field is produced by a single current loop around the equator. Roughly estimate the
You want to get an idea of the magnitude of magnetic fields produced by overhead power lines. You estimate that two wires are each about 30m above the ground and are about 3m apart. The local power
(a) What value of magnetic field would make beak of electrons, traveling ro the right at a speed of 4.8 X 106m/s, go undefeated through a region where there is a uniform electric field of 10,000 V/m
A proton follows a spiral path through a gas in a magnetic field of 0.010T, perpendicular to the plane of the spiral, as shown in Fig. 20-70, in two successive loops, at points P and Q, the radii are
A 32-cm-long solenoid, 1.8cm in diameter, is to produce a 0.30-T magnetic field at its center. If the maximum current is 5.7 A, how many turns must the solenoid have?
Two long straight aluminum wires, each of diameters 0.50mm, carry the same current but in opposite direction. They are suspended by 0.50-m-long strings as shown in Fig. 20-71. If the suspended
An electron enters a uniform magnetic field B = 0.23 T at a 45o angle to B. determine the radius r and pitch p (distance between loops) of the electron€™s helical path assuming its speed is
Calculate the ratio of the electrostatic to gravitational inter-action forces between two electrons, between two protons. At what value of the specific charge q/m of a particle would these forces
What would be the interaction force between two copper spheres, each of mass i g, separated by the distance t m, if the total electronic charge in them differed from the total charge of the nuclei by
Two small equally charged spheres, each of mass m, are suspended from the same point by silk threads of length l. The distance between the spheres x
Two positive charges ql and q2 are located at the points with radius vectors r1 and r2. Find a negative charge q3 and a radius vector r3 of the point at which it has to be placed for the force acting
A thin wire ring of radius r has an electric charge q. What will be the increment of the force stretching the wire if a point charge q0 is placed at the ring's centre?
A positive point charge 50 μC is located in the plane xy at the point with radius vector r0 = 2i + 3j, where i and j are the unit vectors of the x and y axes. Find the vector of the electric
Point charges q and --q are located at the vertices of a square with diagonals 2l as shown in Fig. 3.1. Find the magnitude of the electric field strength at a point located symmetrically with respect
A thin half-ring of radius R = 20 cm is uniformly charged with a total charge q ---- 0.70 nC. Find the magnitude of the electric field strength at the curvature centre of this half-ring.
A thin wire ring of radius r carries a charge q. Find the magnitude of the electric field strength on the axis of the ring as a function of distance l from its centre. Investigate the obtained
A point charge q is located at the centre of a thin ring of radius R with uniformly distributed charge --q. Find the magnitude of the electric field strength vector at the point lying on the axis of
A system consists of a thin charged wire ring of radius and a very long uniformly charged thread oriented along the axis of the ring, with one of its ends coinciding with the centre of the ring. The
A thin non-conducting ring of radius R has a linear charge density λ = λ0 cos φ, where λ0 is a constant, φ is the azimuthal angle. Find the magnitude of the electric field
A thin straight rod of length 2a carrying a uniformly distributed charge q is located in vacuum. Find the magnitude of the electric field strength as a function of the distance r from the rod's
A very long straight uniformly charged thread carries a charge λ per unit length. Find the magnitude and direction of the electric field strength at a point which is at a distance y from the
A thread carrying a uniform charge λ per unit length has the configurations shown in Fig. 3.2 a and b. Assuming a curvature radius R to be considerably less than the length of the thread, find
A sphere of radius r carries a surface charge of density (σ = ar, where a is a constant vector, and r is the radius vector of a point of the sphere relative to its centre. Find the electric
Suppose the surface charge density over a sphere of radius R depends on a polar angle θ as σ = σ0 cos θ, where σ0 is a positive constant. Show that such a charge distribution
Find the electric field strength vector at the centre of a ball of radius R with volume charge density p = ar, where a is a constant vector, and r is a radius vector drawn from the ball's centre.
A very long uniformly charged thread oriented along the axis of a circle of radius R rests on its centre with one of the ends. The charge of the thread per unit length is equal to λ. Find the
Two point charges q and --q are separated by the distance 2l (Fig. 3.3). Find the flux of the electric field strength vector across a circle of radius R.
A ball of radius R is uniformly charged with the volume density p. Find the flux of the electric field strength vector across the ball's section formed by the plane located at a distance r0 < R from
Each of the two long parallel threads carries a uniform charge λ, per unit length. The threads are separated by a distance l. Find the maximum magnitude of the electric field strength in the
An infinitely long cylindrical surface of circular cross-section is uniformly charged lengthwise with the surface density σ = σ0 cos φ, where φ is the polar angle of the
The electric field strength depends only on the x and g coordinates according to the law E = a (xi +yJ)/(x2 + g2), where a is a constant, i and j are the unit vectors of the x and g axes. Find the
A ball of radius R carries a positive charge whose volume density depends only on a separation r from the ball's centre as P = P0 (1 – r/R), where P0 is a constant. Assuming the permittivities of
A system consists of a ball of radius R carrying a spherically symmetric charge and the surrounding space filled with a charge of volume density p = a/r, where a is a constant, r is the distance from
A space is filled up with a charge with volume density p p0 e-r3, where P0 and a are positive constants, r is the distance from the centre of this system. Find the magnitude of the electric field
Inside a ball charged uniformly with 'volume density p there is a spherical cavity. The centre of the cavity is displaced with respect to the centre of the ball by a distance a. Find the field
Inside an infinitely long circular cylinder charged uniformly with volume density p there is a circular cylindrical cavity. The distance between the axes of the cylinder and the cavity is equal to a.
There are two thin wire rings, each of radius R, whose axes coincide. The charges of the rings are q and --q. Find the potential difference between the centers of the rings separated by a distance a.
There is an infinitely long straight thread carrying a charge with linear density λ, = 0.40 μC/m. Calculate the potential difference between points 1 and 2 if point 2 is removed η =
Find the electric field potential and strength at the centre of a hemisphere of radius R charged uniformly with the surface density a.
A very thin round plate of radius R carrying a uniform surface charge density a is located in vacuum. Find the electric field potential and strength along the plate's axis as a function of a distance
Find the potential φ at the edge of a thin disc of radius carrying the uniformly distributed charge with surface density a.
Find the electric field strength vector if the potential of this field has the form φ = at, where a is a constant vector, and r is the radius vector of a point of the field.
Determine the electric field strength vector if the potential of this field depends on x, y coordinates as a) φ = a(x 2 – y2); (b) φ = axy, where a is a constant. Draw the approximate
The potential of a certain electrostatic field has the form φ = a (x2 + Y2) + bz2, where a and b are constants. Find the magnitude and direction of the electric field strength vector. What shape
A charge q is uniformly distributed over the volume of a sphere of radius. Assuming the permittivity to be equal to unity throughout, find the potential (a) At the centre of the sphere; (b) Inside
Demonstrate that the potential of the field generated by a dipole with the electric moment p (Fig. 3.4) may be represented as φ = pr/4πε0r3, where r is the radius vector. Using this
A point dipole with an electric moment p oriented in the positive direction of the z axis is located at the origin of coordinates. Find the projections E, and E.┴ of the electric field strength
A point electric dipole with a moment p is placed in the external uniform electric field whose strength equals Eo, with P ↑↑ E0. In this case one of the equipotential surfaces enclosing
Two thin parallel threads carry a uniform charge with linear densities X and --X. The distance between the threads is equal to l. Find the potential of the electric field and the magnitude of its
Two coaxial rings, each of radius R, made of thin wire are separated by a small distance l (l > R.
Two infinite planes separated by a distance l carry a uniform surface charge of densities σ and = σ (Fig. 3.7). The planes have round coaxial holes of radius R, with l
An electric capacitor consists of thin round parallel plates, each of radius R, separated by a distance l (l > l. Investigate the obtained expressions at x >> R.
A dipole with an electric moment p is located at a distance r from a long thread charged uniformly with a linear density Find the force F acting on the dipole if the vector p is oriented (a) Along
Find the interaction force between two water molecules separated by a distance l = 10 nm if their electric moments are oriented along the same straight line. The moment of each molecule equals p =
Find the potential φ (x, y) of an electrostatic field E = a (yi + xj), where a is a constant, i and j are the unit vectors of the x and y axes.
Find the potential φ (x, y) of an electrostatic field E = a (yi + xj), where a is a constant, i and j are the unit vectors of the x and y axes. Discuss.
Determine the potential φ (x, y, z) of an electrostatic field E = ayi + (ax -4- bz) j + byk, where a and b are constants, i, j, k are the unit vectors of the axes x, y, z.
The field potential in a certain region of space depends only on the x coordinate as φ = ax 3 + b, where a and b are constants. Find the distribution of the space charge p (x).
A uniformly distributed space charge fills up the space between two large parallel plates separated by a distance d. The potential difference between the plates is equal to ∆φ. At what
The field potential inside a charged ball depends only on the distance from its centre as φ = ar2 + b, where a and b are constants. Find the space charge distribution p (r) inside the ball.
A long cylinder with uniformly charged surface and cross-sectional radius a = 1.0 cm moves with a constant velocity = 10 m/s along its axis. An electric field strength at the surface of the cylinder
An air cylindrical capacitor with a dc voltage V = 200 V applied across it is being submerged vertically into a vessel filled with water at a velocity v = 5.0 mm/s. The electrodes of the capacitor
At the temperature 0°C the electric resistance of conductor 2 is η times that of conductor 1. Their temperature coefficients of resistance are equal to a2 and a1 respectively. Find the
Find the resistance of a wire frame shaped as a cube (Fig. 3.35) when measured between points(a) 1-7;(b) 1-2;(c) 1-3. The resistance of each edge of the frame is R?
At what value of the resistance Rx in the circuit shown in Fig. 3.36 will the total resistance between points A and B be independent of the number of cells?
Fig. 3.37 shows an infinite circuit formed by the repetition of the same link, consisting of resistance R1 = 4.0 Ω and R2 = 3.0Ω. Find the resistance of this circuit between points A and
There is an infinite wire grid with square cells (Fig. 3.38). The resistance of each wire between neighbouring joint connections is equal to R0. Find the resistance R of the whole grid between points
A homogeneous poorly conducting medium of resistivity p fills up the space between two thin coaxial ideally conducting cylinders. The radii of the cylinders are equal to a and b, with a < b, the
A metal ball of radius a is surrounded by a thin concentric metal shell of radius b. The space between these electrodes is filled up with a poorly conducting homogeneous medium of resistivity p. Find
The space between two conducting concentric spheres of radii a and b (a < b) is filled up with homogeneous poorly conducting medium. The capacitance of such a system equals C. Find the resistivity of
Two metal balls of the same radius a are located in a homogeneous poorly conducting medium with resistivity p. Find the resistance of the medium between the balls provided that the separation between
A metal ball of radius a is located at a distance l from an infinite ideally conducting plane. The space around the ball is filled with a homogeneous poorly conducting medium with resistivity p. In
Two long parallel wires are located in a poorly conducting medium with resistivity p. The distance between the axes of the wires is equal to l, the cross-section radius of each wire equals a. In the
The gap between the plates of a parallel-plate capacitor is filled with glass of resistivity p = 100 GΩ ∙ m. The capacitance of the capacitor equals C = 4.0nF. Find the leakage current of
Two conductors of arbitrary shape are embedded into an infinite homogeneous poorly conducting medium with resistivity p and permittivity e. Find the value of a product RG for this system, where R is
A conductor with resistivity p bounds on a dielectric with permittivity e. At a certain point A at the conductor's surface the electric displacement equals D, the vector D being directed away from
The gap between the plates of a parallel-plate capacitor is filled up with an inhomogeneous poorly conducting medium whose conductivity varies linearly in the direction perpendicular to the plates
Demonstrate that the law of refraction of direct current lines at the boundary between two conducting media has the form tan az/tan a1 = σ2/σl, where σ1 and σ2 are the
Two cylindrical conductors with equal cross-sections and different resistivity p1 and p2 are put end to end. Find the charge at the boundary of the conductors if a current I flows from conductor I to
The gap between the plates of a parallel-plate capacitor is filled up with two dielectric layers I and 2 with thicknesses d1 and d2, permittivities ε1 and ε2, and resistivity Pl and p2. A
An inhomogeneous poorly conducting medium fills up the space between plates 1 and 2 of a parallel-plate capacitor. Its permittivity and resistivity vary from values el, Pl at plate 1 to values
The space between the plates of a parallel-plate capacitor is filled up with inhomogeneous poorly conducting medium whose resistivity varies linearly in the direction perpendicular to the plates. The
A long round conductor of cross-sectional area S is made of material whose resistivity depends only on a distance r from the axis of the conductor as p = az/r2, where a is a constant. Find: (a) The
A capacitor with capacitance C = 400 pF is connected via a resistance R = 650 f2 to a source of constant voltage V0. How soon will the voltage developed across the capacitor reach a value V = 0.90 V0?
A capacitor filled with dielectric of permittivity ε = 2.1 loses half the charge acquired during a time interval τ = 3.0 min. Assuming the charge to leak only through the dielectric filler,
A circuit consists of a source of a constant emf ε and a resistance R and a capacitor with capacitance C connected in series. The internal resistance of the source is negligible. At a moment t =
An ammeter and a voltmeter are connected in series to a battery with an emf ε = 6.0 V. When a certain resistance is connected in parallel with the voltmeter, the readings of the latter decrease

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