1.Convert the following vectors to cylindrical and spherical systems: F = 10,+ya, +za, G = *+y*...

 

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1.Convert the following vectors to cylindrical and spherical systems: F = 10,+ya, +za, G = *+y* [ra, + ya, + za:] 2.The acceleration of a particle is given bya = 2.4a,m/s. The initial position of the particle is r = (0, 0, 0), while its initial velocity isu =-2a, + 5a,m/s. (a) Find the position of the particle at time t = 1. (b) Determine the velocity of the particle as a function of t 3.Prove that (1) V• (VA) = VV• A+ A•VV where V is a scalar field and A is a vector field, (2) Evaluate V. (VA) whenA 2ray + 3yay - 4zazand V = ryz. Let A = psinda, + pas. Evaluate f, A• dl given that (1) L is contour given fig 1.0 fig 1.0 4.A charge distribution in free space hasp, = 2rnC/m³ for 0 <rs 10mand zero otherwise. Determine E at r= 2m andr 12m. 5.Ring placed along y? + z? = 4, x = 0 carries a uniform charge of 5 µC/m. (1) Find D at P(3,0, 0). (2) If two identical point charges Q are placed at(0,-3,0)and (0,3,0) in ad- dition to the ring.find the value of Q such that D = 0 at P. 2. 1.Convert the following vectors to cylindrical and spherical systems: F = 10,+ya, +za, G = *+y* [ra, + ya, + za:] 2.The acceleration of a particle is given bya = 2.4a,m/s. The initial position of the particle is r = (0, 0, 0), while its initial velocity isu =-2a, + 5a,m/s. (a) Find the position of the particle at time t = 1. (b) Determine the velocity of the particle as a function of t 3.Prove that (1) V• (VA) = VV• A+ A•VV where V is a scalar field and A is a vector field, (2) Evaluate V. (VA) whenA 2ray + 3yay - 4zazand V = ryz. Let A = psinda, + pas. Evaluate f, A• dl given that (1) L is contour given fig 1.0 fig 1.0 4.A charge distribution in free space hasp, = 2rnC/m³ for 0 <rs 10mand zero otherwise. Determine E at r= 2m andr 12m. 5.Ring placed along y? + z? = 4, x = 0 carries a uniform charge of 5 µC/m. (1) Find D at P(3,0, 0). (2) If two identical point charges Q are placed at(0,-3,0)and (0,3,0) in ad- dition to the ring.find the value of Q such that D = 0 at P. 2.