Solved Problems-Ch30 - Sources of Magnetic Field- New

Ch-30 Problems and Solutions Phy201 – Dr. Hikmat A. Hamad 1. Calculate the magnitude of the magnetic field at a point 25.0 cm from a long, thin

conductor carrying a current of 2.00 A.

2. (a) A conducting loop in the shape of a square of edge length, ℓ= 0.400 m carries a current

I = 10.0 A as shown in Figure P30.5. (a) Calculate the magnitude and direction of the magnetic field at the center of the square. (b) What If? If this conductor is reshaped to form a circular loop and carries the same current, what is the value of the magnetic field at the center?

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3. An infinitely long wire carrying a current I is bent at a right angle as shown in Figure

P30.6. Determine the magnetic field at point P, located a distance x from the corner of the wire.

4. A conductor consists of a circular loop of radius R= 15.0 cm and two long, straight

sections as shown in Figure P30.7. The wire lies in the plane of the paper and carries a current I = 1.00 A. Find the magnetic field at the center of the loop.

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5. In Figure P30.23, the current in the long, straight wire is I1 = 5.00 A and the wire lies in

the plane of the rectangular loop, which carries a current I2 = 10.0 A. The dimensions in the figure are c = 0.100 m, a = 0.150 m, and , ℓ= 0.450 m. Find the magnitude and direction of the net force exerted on the loop by the magnetic field created by the wire.

6. Four long, parallel conductors carry equal currents of I =5.00 A. Figure P30.32 is an end

view of the conductors. The current direction is into the page at points A and B and out of the page at points C and D. Calculate (a) the magnitude and (b) the direction of the magnetic field at point P, located at the center of the square of edge length , ℓ = 0.200 m.

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7. A long, cylindrical conductor of radius R carries a current I as shown in Figure P30.36. The current density J, however, is not uniform over the cross section of the conductor but rather is a function of the radius according to J = br, where b is a constant. Find an expression for the magnetic field magnitude B (a) at a distance r1 R, measured from the center of the conductor.

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8. A long solenoid that has 1 000 turns uniformly distributed over a length of 0.400 m produces a magnetic field of magnitude 1.00 x 10-4 T at its center. What current is required in the windings for that to occur?

9. A cube of edge length ,ℓ= 2.50 cm is positioned as shown in Figure P30.45. A uniform

magnetic field given by 𝐵𝐵 = (5𝑖𝑖 + 4𝑗𝑗 + 3k) exists throughout the region. (a) Calculate the magnetic flux through the shaded face. (b) What is the total flux through the six faces?

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10. Consider the hemispherical closed surface in Figure P30.46. The hemisphere is in a uniform magnetic field that makes an angle θ with the vertical. Calculate the magnetic flux through (a) the flat surface S1 and (b) the hemispherical surface S2.

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11. One long wire carries a current of 30A along the entire x axis. A second long wire carries a current of 40A perpendicular to the xy plane and passes through the point (0,4,0)m. What is the magnitude of the resulting magnetic field at the point y=2m on the y-axis Ans.5 µT

12. Two long parallel wires each carry a current of 5.0 A directed to the east. The two wires are separated by 8.0 cm. What is the magnitude of the magnetic field at a point that is 5.0 cm from each of the wires? Ans: 24 μT

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13. Each of two long straight parallel wires separated by a distance of 16 cm carries a current of 20 A in the same direction. What is the magnitude of the resulting magnetic field at a point that is 10 cm from each wire? Ans: 48 µT (From the review problems)

14. A hollow cylindrical (inner radius = 1.0 mm, outer radius = 3.0 mm) conductor carries a current of 80 A parallel to its axis. This current is uniformly distributed over a cross section of the conductor. Determine the magnitude of the magnetic field at a point that is 2.0 mm from the axis of the conductor. Ans:3.0 mT 𝑨𝑨/ = 𝝅𝝅�𝟎𝟎. 𝟎𝟎𝟎𝟎𝟎𝟎)𝟐𝟐 − (𝟎𝟎. 𝟎𝟎𝟎𝟎𝟎𝟎)𝟐𝟐 � = 𝟗𝟗. 𝟒𝟒𝟒𝟒𝟒𝟒𝟏𝟏𝟏𝟏−𝟔𝟔 𝒎𝒎𝟐𝟐

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15. Two long straight parallel wires separated by a distance of 20 cm carry currents of 30 A and 40 A in opposite directions. What is the magnitude of the resulting magnetic field at a point that is 15 cm from the wire carrying the 30-A current and 25 cm from the other wire? Ans: 33 μT

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