1 A very long line of charge has a linear charge density of 12.5 µC/m. A point charge with a charge of 63.4 µC is placed 0.720 m away from the line of charge. In the space between the line and charge, there is a point where the electric field is zero. How far away from the line of charge is this point?
4 The vertical velocity of a particle on a string is expressed by vy(x,t) = 2.55 (m/s)cos(3.45x +32.4t). (a) What is the expression of the vertical displacement of the string? (b) What is the wavelength of the string’s oscillation? (c) If the linear density of the string is 0.105 kg/m, find the tension in the string.
8 A dust particle having a charge of -12.6 µC and mass m = 1.68 pg, is observed to move with a velocity of ν = 1.36×104 m/s in a region of a uniform magnetic field (within the dotted square in the diagram). It travels counterclockwise on a circular path of 9.28-cm diameter. The motion is without friction in the horizontal plane- you may consider it to be the plane of the page/screen-. What are the magnitude and direction (into or out of the page) of the magnetic field in this region?
9 (a) A rectangular loop 30.0 cm x 40.0 cm is located inside a region of a spatially uniform magnetic as shown in the figure with the magnetic field perpendicular to the plane of the loop. Determine the magnitude and direction (clockwise or counterclockwise, you must justify by analysis of relevant laws or principles in physics) of the induced current if the resistance of the loop is 0.150 Ω, and the magnetic field is increasing at a constant rate of 0.0750 T/s? (6 points)
(b) Now if the magnetic field is kept constant at 0.75 T and the loop is pulled out at a constant speed of 2.00 cm/s traveling perpendicular to the field lines. Determine the magnitude and direction (clockwise or counterclockwise, you must justify by analysis of relevant laws or principles in physics) of the induced current when, (i) the loop is totally in the magnetic field’s region, and (ii) when right side of the loop starts to depart the region of the magnetic field. (6 points)