(a) A charge -330 e isuniformly distributed along a circular arc of radius 4.90

Question

(a) A charge -330e isuniformly distributed along a circular arc of radius 4.90 cm, whichsubtends an angle of 41o. What is the linear chargedensity along the arc? (b) A charge-330e is uniformly distributed over one face of acircular disk of radius 4.30 cm. What is the surface charge densityover that face?(c) A charge-330e is uniformly distributed over the surface of asphere of radius 2.50 cm. What is the surface charge density overthat surface? (d) A charge-330e is uniformly spread through the volume of asphere of radius 3.30 cm. What is the volume charge density in thatsphere?

Explanation / Answer

In each case , charge =-330e =-330*1.6*10-19 =-5.28*10-17 C a )Here total length of ring = r Here =41o = 0.716 rad So length of ring = 0.716*0.0490 = 0.035 m So charge density = charge / length = -5.28*10-17/0.035= -1.506*10-15 C/m b)Here the charge is spread on area Area = r2= 5.809*10-3 m2 So surface charge density = charge /area = -5.28*10-17/5.809*10-3 =-9.09*10-15 C/m2 c)Here charge is spread on surface of sphere So surface area = 4r2=1.505*10-4m3 So volume charge density = charge /volume = -5.28*10-17/1.505*10-4 =-3.507*10-13 C/m3 d)Here charge is spread in volume of sphere So Volume = 4r3/3=7.85*10-3m2 So surface charge density = charge /area = -5.28*10-17/7.85*10-3 =-6.72*10-15 C/m2

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