Question 1: An infinitesimal current element Idl is located at the point x = 0.05m, y =0, z = 0 in a cartesian coordinate system. The current element points in the direction of the positive z-axis and has magnitude 2x10^-6 A m. Calculate the magnitude and direction of the magnetic field due to this current element at the point x = 0.1m, y = 0, z = 0.2 m.
Question 2: Consider two long straight, parallel wires. One wire is located along the z-axis of a cartesian coordinate system, the other intersects the z = 0 plane at the point x = D, y = 0 (D > 0). Each wire has radius a (where a < D) and each carries current I in the z -direction. The current density is uniform in each wire. Apply the principle of superposition to determine the magnetic field B at the point (x, 0, 0), where 0 (less than or equal to) x (less than or equal to) D. Distinguish between the cases 0 (less than or equal to) x (less than or equal to) a, a < x < D-a and D-a (less than or equal to) x (less than or equal to) D.
Question 3: A vector field is given by the expression,
E = A(x e_x + y e_y + z e_z)/(x^2 + y^2 + z^2)^(5/2)
Where A > 0 is a constant.
a) Could this vector field represent an electric field?
b) Show that if E is an electric field the corresponding electrostatic potential can be written as,
V(r) = A/3r^3
c) A particle with mass m and electric charge q < 0 executes a circular orbit in the z = 0 plane, with centre at the origin and radius Ro. The particle moves anticlockwise (as seen from above the z =0 plane) with constant speed,
v = _/(-q)RoEr(Ro)/m
such that the electric force provides the required centripetal acceleration. The electric field is then replaced with a uniform magnetic field B. Calculate the direction and magnitude of B so that the circular motion of the particle remains unchanged.
Step-by-step solution that calculates the magnitude and direction of the magnetic field due to the current element is provided.