A current i is passed through a silver strip of width d and area of cross section A. The number of free electrons per unit volume is π.

(a) Find the drift velocity v of the electrons.

(b) If a magnetic field B exists in the region as shown in figure, what is the average magnetic force on the free electrons?

(c) Due to the magnetic force, the free electrons get accumulated on one side of the conductor along its length. This produces a transverse electric field in the conductor which opposes the magnetic force on the electrons. Find the magnitude of the electric field which will stop further accumulation of electrons.

(d) What will be the potential difference developed across the width of the conductor due to the electron-accumulation? The appearance of a transvers emf, when a current carrying wire is placed in a magnetic field, is called Hall effect.

A rectangular coil of 100 turns has length 5 cm and width 4 cm. It is placed with its plane parallel to a uniform magnetic field and a current of 2A is sent through the coil. Find the magnitude of the magnetic field B, if the torque acting on the coil is 0.2 N m^–1.

A circular coil of radius 2.0 cm ahs 500 turns in it and carries a current of 1.0 A. Its axis makes an angle of 30° with the uniform magnetic field of magnitude 0.40 T that exist in the space. Find the torque acting on the coil.

A rectangular loop of sides 20 cm and 10 cm carries a current of 5.0 A. A uniform magnetic field of magnitude 0.20 T exists parallel to the longer side of the loop.

(a) What is the force acting on the loop?

(b) What is the torque acting on the loop?

A circular loop carrying a current i has wire of total length L. A uniform magnetic field B exists parallel to the plane of the loop.

(a) Find the torque on the loop.

(b) If the same length of the wire is used to form a square loop, what would be the torque? Which is larger?

Fe⁺ions are acceleration through a potential difference of 500 V and are injected normally into a homogeneous magnetic field B of strength 20.0 mT. Find the radius of the circular paths followed by the isotopes with mass numbers 57 and 58. Take the mass of an ion = A(1.6 × 10^–27) kg where A is the mass number.

Let and denote electric and magnetic fields in a frame S. and in another frame S’ moving with respect to S at a velocity Two of the following equations are wrong. Identify them.

Consider three quantities x = E/B, y = and . Here, ℓ is the length of a wire, C is a capacitance and R is a resistance. All other symbols have standard meanings.

A narrow beam of singly charged potassium ions of kinetic energy 32 keV is injected into a region of width 1.00 cm having a magnetic field of strength 0.500 T as shown in figure. The ions are collected at a screen 95.5 cm away form the field region. If the beam contains isotopes of atomic weights 39 and 41, find the separation between the points where these isotopes strike the screen. Take the mass of a potassium ion = A(1.6 × 10^–27) kg where A is the mass number.

A particle having mass m and charge q is release from the origin in a region in which electric field and magnetic field are given by

Find the speed of the particle as a function of its z-coordinate.