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Poynting Vector: E and B Fields In EM Waves

Q- A radio transmitter on the Earth’s surface radiates a sinusoidal wave with an average total power of 50 kW. Assuming that the transmitter radiates equally in all directions above the ground calculate the amplitudes Emax and Bmax detected by a satellite positioned 100 km from the transmitter.

S…

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Electromagnetic Waves

Q1- How much time is required for a radio signal to travel from Earth to a space station on Mars if the planet Mars is 7.83 x 107 km from Earth?  

Q2- The speed of light through a transparent substance is 2.00 x 108 m/s. What is the index of refraction of the substance?

Q3- A monochromatic light …

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LR Circuit

Q- The switch for the network of Figure has been closed for long time. It is then opened at the time defined as t = 0 s

(a) Determine the time required for the current Ito drop to 1 mA.

(b) Find the voltage Vat t = 1 ms.

(c) Calculate at t = 5 τ (time constant).

Solution:

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Electromagnetic Induction

Q- A square conducting loop with sides length a = 0.5 m is placed in a magnetic field. The magnetic field varies in time according to the graph. If the area vector of the coil is in the same direction as magnetic field, what is the magnitude of the induced EMF in the coil at t = 25 s, 35 s and 60 s?…

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Electromagnetic Induction

Q- A solenoid has length L = 30 cm, radius 6 cm, and N1 = 5500 turns; its axis coincides with the z-axis. A circular conducting loop containing N2 = 15 turns of radius a = 3 cm is centered inside the solenoid; the plane of the loop makes a 30° angle with respect to the z-axis. The loop has a net res…

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Electromagnetic Induction

Q-A one-turn rectangular loop oriented parallel to the x-y plane and having dimensions a = 2 cm, b = 11 cm moves with a constant velocity v = 20 m/s in the +x direction. An external agent (force) ensures that this velocity remains constant throughout the motion. The wire of which the loop is made ha…

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Electromagnetic Induction: Wire on rails

Q- A rod of length L caused to move at a constant speed v along horizontal conducting rails. The magnetic field B is not constant, but is supplied by a long wire parallel to the conducting rails. This wire is a distance a from the rail and has a current i.  If L = 3.18 cm, v = 4.61 m/s, a = 10.8 mm…

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Electromagnetic waves

Q- The intensity of sunlight striking the earth's upper atmosphere (called the solar constant) is 1.35 kW/m2.

(a) Find Erms and Brms due to the sun at the upper atmosphere of the earth.

(b) Find the average power output of the sun

(c) Find the intensity at the surface of the sun. 

(d) Find th…

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Magnetic Flux

Q- Find the total flux linkage of the coil shown in figure if each flux line represents 2*10-7 Wb.

(a)What is the equivalent flux linking all of the turns in Figure?

(b) What is the flux linking per turn?

Solution:

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Electromagnetic Induction: Solenoid

Q- A solenoid has length L = 30 cm, radius 6 cm, and N1 = 5500 turns; its axis coincides with the z-axis. A circular conducting loop containing N2 = 15 turns of radius a = 3 cm is centered inside the solenoid; the plane of the loop makes a 30° angle with respect to the z-axis. The loop has a net res…

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Electromagnetic Waves

Q- A vertically polarized radio wave of frequency 9.0*105 Hz traveling into the page. The maximum electric field strength is 1250 V/m. 

(a) What is the maximum magnetic field strength?

(b) What is the magnetic field strength and direction at a point where electric field is E = 625 V/m, downward? …

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Transformers

Q1- A step-up transformer has a primary coil with 100 loops and a secondary coil with 1,500 loops. If the primary coil is supplied with a household current of 120 V and 15 A,

(a) what voltage is produced in the secondary circuit?

(b) What current flows in the secondary circuit?

Q2- The step-down …

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Magnetic Field: Coaxial Cable.

Q- An infinite cylindrical conductor of radius a = 1 cm carries a current I1 = 0.3 A out of the page. A coaxial, infinite, thin cylindrical conducting shell of radius b = 5 cm carries a current I2 = 0.12 A, into the page. The current densities in each conductor are uniform.

(a) Calculate the magnit…

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Magnetic Field: Torus

Q- A circular torus has inner radius R1 = 30 cm, outer radius R2 = 50 cm, and N = 710 turns wound uniformly around it. The current in the windings is I = 3 A.

(a) Calculate the magnitude of the magnetic field B, inside the torus, in the symmetrical plane along the inner and outer diameter, at the f…

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Electromagnetism

Q- A wire frame in the shape of an equilateral triangle of side d = 8 cm, carries current i = 0.25 A. This frame is located in a region of space that contains a constant magnetic field of magnitude B = 1.3 T, Normal to the plane of the frame and the frame is in stable equilibrium. What is the work y…

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Electromagnetism

Q- An electron is moving straight towards a long straight wire with a velocity of 2*107 m/s. When the electron is 6 cm from the wire, a current I = 12 A suddenly appears in the wire. Find

(a) The magnitude and direction of the of the magnetic field of this current at the position of the electron.

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Electromagnetic induction

Q- A long straight wire carrying a current of I1 = 30 A is paced in the plane of a rectangular wire loop and parallel to its nearest side of length l = 30 cm, at a distance of a = 1 cm. The width of the loop is b = 8 cm. Find the magnitude of the net force on the loop if the current in the loop is I

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Electromagnetic Induction

Q- A circular loop with radius a = 0.35 m and N = 21 turns lies in the plane of the page. The wire used in constructing the loop has a resistance per unit length of dR/dl = 0.11 W/m. A spatially uniform magnetic field points into the page. In the interval between t = 0 and 10 s, the strength of this…

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Electromagnetic induction

Q- A circular loop of radius a = 20 cm and N=168 turns is fixed in the x-y plane. A spatially uniform magnetic field with only -component covers the entire area of the loop. The plot bellow shows Bz measured in Tesla versus time t measured in seconds. The +z direction is OUT of the screen.

(a) …

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Electromagnetism: Induced EMF

Q- A solenoid has length L = 30 cm, radius 6 cm, and N1 = 5500 turns; its axis coincides with the z-axis. A circular conducting loop containing N2 = 15 turns of radius a = 3 cm is centered inside the solenoid; the plane of the loop makes a 30° angle with respect to the z-axis. The loop has a net res…

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