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10) Two coplanar and concentric circular loops of wire carry currents of I1 = 5.30 A and I2 = 2.80 A in opposite directions as in the figure below. Let r1 = 12.0 cm and r2 = 8.50 cm. (Assume the positive direction along the axis perpendicular to the faces of the loops is out of the screen (towards you) and assume the positive vertical direction is toward the top of the screen.) (a) What is the magnitude of the net magnetic field (in ?T) at the center of the two loops? (b) What is the direction of the net magnetic field at the center of the two loops? (c) Let r1 remain fixed at 12.0 cm and let r2 be a variable. Determine the value of r2 (in cm) such that the net field at the center of the loops is zero. Ans: (a) 7.05 ?T, (b) into the page, (c) 6.34 cm 11) A rectangular loop of area A is placed in a region where the magnetic field is perpendicular to the plane of the loop. The magnitude of the magnetic field is allowed to vary in time according to B = B_max e^{-t/?}, where B_max and ? are constants, and t ? 0. For times t < 0, the field has the constant value B_max. Find the emf induced in the loop as a function of time. Ans: ? = (A B_max/?) e^{-t/?} 12) Consider the apparatus shown: a conducting bar is moved along two rails connected to an incandescent lightbulb. The whole system is immersed in a magnetic field of magnitude B = 0.400 T perpendicular to the page and pointing into it. The distance between the horizontal rails is ? = 0.800 m. The resistance of the lightbulb is R = 48 ?, assumed to be constant. The bar and rails have negligible resistance. The bar is moved toward the right by a constant force of magnitude F = 0.600 N.

          10) Two coplanar and concentric circular loops of wire carry currents of I1 = 5.30 A and I2 = 2.80 A in opposite directions as in the figure below. Let r1 = 12.0 cm and r2 = 8.50 cm. (Assume the positive direction along the axis perpendicular to the faces of the loops is out of the screen (towards you) and assume the positive vertical direction is toward the top of the screen.) (a) What is the magnitude of the net magnetic field (in ?T) at the center of the two loops? (b) What is the direction of the net magnetic field at the center of the two loops? (c) Let r1 remain fixed at 12.0 cm and let r2 be a variable. Determine the value of r2 (in cm) such that the net field at the center of the loops is zero.
Ans: (a) 7.05 ?T, (b) into the page, (c) 6.34 cm

11) A rectangular loop of area A is placed in a region where the magnetic field is perpendicular to the plane of the loop. The magnitude of the magnetic field is allowed to vary in time according to B = B_max e^{-t/?}, where B_max and ? are constants, and t ? 0. For times t < 0, the field has the constant value B_max. Find the emf induced in the loop as a function of time. Ans: ? = (A B_max/?) e^{-t/?}

12) Consider the apparatus shown: a conducting bar is moved along two rails connected to an incandescent lightbulb. The whole system is immersed in a magnetic field of magnitude B = 0.400 T perpendicular to the page and pointing into it. The distance between the horizontal rails is ? = 0.800 m. The resistance of the lightbulb is R = 48 ?, assumed to be constant. The bar and rails have negligible resistance. The bar is moved toward the right by a constant force of magnitude F = 0.600 N.

10) Two coplanar and concentric circular loops of wire carry currents of I1 = 5.30 A and I2 = 2.80 A in opposite directions as in the figure below. Let r1 = 12.0 cm and r2 = 8.50 cm. (Assume the positive direction along the axis perpendicular to the faces of the loops is out of the screen (towards you) and assume the positive vertical direction is toward the top of the screen.) (a) What is the magnitude of the net magnetic field (in ?T) at the center of the two loops? (b) What is the direction of the net magnetic field at the center of the two loops? (c) Let r1 remain fixed at 12.0 cm and let r2 be a variable. Determine the value of r2 (in cm) such that the net field at the center of the loops is zero.
Ans: (a) 7.05 ?T, (b) into the page, (c) 6.34 cm

11) A rectangular loop of area A is placed in a region where the magnetic field is perpendicular to the plane of the loop. The magnitude of the magnetic field is allowed to vary in time according to B = Bmax e^-t/?, where Bmax and ? are constants, and t ? 0. For times t < 0, the field has the constant value Bmax. Find the emf induced in the loop as a function of time. Ans: ? = (A Bmax/?) e^-t/?

12) Consider the apparatus shown: a conducting bar is moved along two rails connected to an incandescent lightbulb. The whole system is immersed in a magnetic field of magnitude B = 0.400 T perpendicular to the page and pointing into it. The distance between the horizontal rails is ? = 0.800 m. The resistance of the lightbulb is R = 48 ?, assumed to be constant. The bar and rails have negligible resistance. The bar is moved toward the right by a constant force of magnitude F = 0.600 N.

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