NYJC_EJC 2026 Electric and Magnetic Fields Tutorial

9814 H3 Physics (2026) 1 Electric and Magnetic Fields tutorial 1 The six faces of a cubical box each measure 20.0 cm by 20.0 cm, and the faces are numbered such that faces 1 and 6 are opposite to each other, as are faces 2 and 5, and faces 3 and 4. The flux through each face is given in the table. Determine the net charge inside the cube. face flux / N m2 C−1 1 −70.0 2 −300.0 3 −300.0 4 300.0 5 −400.0 6 −500.0 2 Electric fields of varying magnitudes are directed either inward or outward at right angles on the faces of a cube, as shown in Fig. 2.1. Fig. 2.1 Determine the strength and direction of the field on the face F. 3 A −6.00 nC point charge is located at the centr e of a conducting spherical shell. The shell has an inner radius of 2.00 m, an outer radius of 4.00 m, and a charge of 7.00 nC. (a) Determine (i) the electric field at r = 1.00 m, (ii) the electric field at r = 3.00 m, (iii) the electric field at r = 5.00 m. (b) Calculate the surface charge distribution, , on the outside surface of the shell. 4 A hollow conducting spherical shell has an inner radius of 8.00 cm and an outer radius of 10.0 cm. The electric field at the inner surface of the shell has a magnitude of 80.0 N C −1 and points toward the centre of the sphere, and the electric field at the outer surface has a magnitude of 80.0 N C−1 and points away from the centre of the sphere. Determine the charge on the inner surface and on the outer surface of the spherical shell. 5 Two parallel, infinite, non-conducting plates are 10.0 cm apart and have charge distributions of 1.00 C m−2 and –1.00 C m−2. Calculate the force on an electron (a) in the space between the plates,

9814 H3 Physics (2026) 2 (b) located outside the two plates near the surface of one of the two plates. 6 Two parallel, uniformly charged, infinitely long wires are 6.00 cm apart and carry opposite charges with a linear charge density of 1.00 C m−1. Determine the magnitude and direction of the electric field at a point midway between the two wires and 40.0 cm above the pla ne containing them. 7 A thin, hollow, metal cylinder of radius R has a surface charge distribution . A long, thin wire with a linear charge density 2  runs through the centre of the cylinder. Determine an expression for the electric field and determine the direction of the field at each of the following locations: (a) rR (b) rR 8 Two infinite sheets of charge are separated b y 10.0 cm as shown in Fig. 9.1 . Sheet 1 has a surface charge distribution of 2 1 3.00 C m −= and sheet 2 has a surface charge distribution of 2 1 5.00 C m −=− . Determine the total electric field at (a) P, 6.00 cm to the left of sheet 1, (b) P’, 6.00 cm to the right of sheet 1. Fig. 9.1 9 A non-conducting sphere has a uniform volume charge density . Let r be the vector from the centre of the sphere to a general point P within the sphere. (a) Show th