Target Audience: High School Students, College Freshmen and Sophomores, students preparing for the International Baccalaureate (IB), AP Physics B, AP Physics C, A Level, Singapore/GCE A-Level;
The total Electromagnetic force on a moving charge, called Lorentz force is given by F = q E + q[v × B] where B is the magnetic force intensity vector which characterizes the magnetic force. The above law is universal, i.e, it is applicable even for varying electric and magnetic ﬁelds and for all velocities of the moving charge.
Basic Laws of Magnetic Field and their applications
• Gauss theorem for B: The Flux of B through any closed surface is zero
• Theorem on circulation of B or Ampere’s Circuital Law
• Theorem on circulation of B is used to calculate magnetic ﬁelds in symmetric situations like long straight conductor, inﬁnitely long solenoid, toroid, large current carrying plane etc. using the symmetry.
• Lenz Law : It states that the induced current is directed such that it’s magnetic ﬂux opposes the original change in magnetic ﬂux.
• Faraday’s Law of EMI : The e.m.f induced in a loop, whatever the cause of it, is given as ξi = − dφ/dt measured in Weber/s.
• e.m.f is caused by time-variant magnetic ﬁeld or by the motion of loop in a space-variant magnetic ﬁeld.
• φ = LI, where L is the inductance of the circuit, which depends on the shape and size of the loop, measured in Henry.
• The presence of magnetic coupling between two circuits leads to Mutual Induction. e.m.f. is induced in one circuit due to change in current in other circuit.
Q: Consider a long straight uniform cylinder of radius R. A direct current of density J ﬂows along the length of cylinder. A cylindrical cavity of radius r is carved out from the cylinder as shown in the cross-section. Find the magnetic ﬁeld in the cavity.
Q: In the ﬁgure shown, a coil of single turn is wound on a sphere of radius r and mass m. The plane of coil is parallel to the inclined plane and lies in the equatorial plane of the sphere. If sphere is in rotational equilibrium, Find the value of B. Let i be the counter-clockwise current through the coil when observed from the top.
Q: Three rings, each having equal radius R, are placed mutually perpendicular to each other and each having it’s center at the origin of the co-ordinate system. If current I ﬂows through each ring, ﬁnd the magnitude of magnetic ﬁeld at the common center i.e, origin.