An electrical dipole, made of two small charged conducting balls stuck to the ends of an insulating bar, is located near an infinite uniformly chamed sheet. It can be in one of the three positions marked A, B, or C, which are distances d, 2d and 3d from the centre of the dipole. The sheet (on the right, coloured orange/yellow) is perpendicular to the page (in the yz plane), and the dipole is in the plane of the page (the X-y plane). Note that when the dipole is at distance 2d it is tipped at an angle of 30 relative to the y axis. .V x 2 d d 933 .9 s C B A 1. [1.5 pts] Copy the picture onto your submission page. For each of the three positions that the dipole can assume, draw a vector representing the dipole moment vector. 2. [2 pts] If the quantities q = 1 uC, -q = -1uC and s = 0.5 cm, what is the magnitude of the dipole moment for each position? Express it in proper SI units. 3. [3 pts] Write the vector for the dipole moment in each position, in component form: PA = ( Cm) it ( Cm) j + ( C m) k PB = ( Cm)it( Cm) j+ ( C m) k Pc = ( Cm) it( Cm) j+( C m) k 4. [3 pts] For each dipole position, draw the direction of the force vector due to the charged sheet on the +q and -q charges. Make all of the vectors to the same scale, so that their relative sizes can be assessed. 5. [2 pts] The surface charge density on the plane is 1=+250 uC/cm2. What is the magnitude of the electrical force on each charged particle, for each position A, B and C. 6. [1.5 pts] What is the total electrical force exerted on the dipole when it is at positions A, B and C? Note that this is the vector sum of all forces on the dipole in a given position. F total, A = ( Nit ( N K F total.B = ( N)it( N) k F total,C = ( N)it ( N) k 7. [3 pts] Now calculate the total torque on the dipole when it is at positions A, B and C. TA = ( Nm) it( N m) j + ( N m) k TB = ( Nm) it ( N m) j + ( N m) k to = ( N m) it( N m) j + ( N m) k 8. [3 pts] Based on your results from the above work, briefly describe how the dipole would respond to the electric field it experiences in each position. Will it experience an overall acceleration, and if so in which direction? Will it experience a tendency to rotate, and if so in what direction? 9. [3 pts] Now the dipole is placed in another region of space. The electric field at the location of the +q and -q charges is indicated on the diagram below. Will the dipole experience an overall acceleration, and if so in which direction? Will it experience a tendency to rotate, and if so in what direction? (Keep the same coordinate axes as on the previous page.) E top S E bottom