Two bar very narrow magnets are located in the x-y plane. Magnet #1 lies on the

Question

Two bar very narrow magnets are located in the x-y plane. Magnet #1 lies on the x-axis and its north end is at x = 1.0cm , while its south end is at x = 5.0 cm.
Magnet #2 lies on the y-axis and its north end is at y = 1.0cm , while its south end is at y = 5.0 cm. Magnet #2 produces a magnetic field that is only one-third the magnitude of magnet #1.

Part A: In what direction would a compass point if it were located at the origin? theta=______degrees below the negative x axis


Part B: Repeat part A for the situation where magnet #1 is reversed in polarity. theta=________degrees above the positive x axis.

Explanation / Answer

magnetic field B1 due to magnet 1 is along -ve x-axis magnetic field B2 due to magnet 2 is along -ve y-axis hence,the mgnetic field is               B = -B1 x^ -B2 y^ the magnetic field due to magnet 2 is B2 = B1/3 therefore,             B = -B1 x^ - (B1/3) y^ therefore, magnetic field B makes an angle with the negative x-axis is           tan = -(B1/3) / (-B1)       angle = tan-1[1/3]                  = 18.430 below the negative x-axis below the negative x-axis .............................................................. magnetic field B1 due to magnet 1 is along +ve x-axis magnetic field B2 due to magnet 2 is along -ve y-axis the mgnetic field is               B = B1 x^ + B2 y^ the magnetic field due to magnet 2 is B2 = B1/3 therefore,             B = -B1 x^ + (B1/3) y^ therefore, magnetic field B makes an angle with the positive x-axis is           tan = (B1/3) / (-B1)       angle = tan-1[-1/3]                  = -18.430 above the positive x axis = 18.430.
magnetic field B1 due to magnet 1 is along +ve x-axis magnetic field B2 due to magnet 2 is along -ve y-axis magnetic field B1 due to magnet 1 is along +ve x-axis magnetic field B2 due to magnet 2 is along -ve y-axis the mgnetic field is               B = B1 x^ + B2 y^ the magnetic field due to magnet 2 is B2 = B1/3 therefore,             B = -B1 x^ + (B1/3) y^ therefore, magnetic field B makes an angle with the positive x-axis is           tan = (B1/3) / (-B1)       angle = tan-1[-1/3]                  = -18.430 above the positive x axis = 18.430.
above the positive x axis = 18.430.

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