The magnetic field due to a long straight wire has been derived in terms of `mu_0`,i and d. Express this in terms of `varepsilon_0`, c, I, and d.

Stopping distance of vehicles : When brakes are applied to a moving vehicle, the distance it travels before stopping is called stopping distance. It is an important factor for road safety and depends on the initial velocity (upsilon_(0)) and the braking capacity, or deceleration, -a that is caused by the braking. Derive an expression for stopping distance of a vehicle in terms of upsilon_(0) and a.

At a distance of 10 cm from a long straight wire carrying current, the magnetic field is 0.04 T. At the distance of 40 cm, the magnetic field will be ______ .

Explain experiment which produced magnetic field due to straight long current carrying wire.

When electric current I flow through a straight wire of length I placed in a magnetic field , a magnetic force of 1N acts on it . If magneitude of the electric current is halved and the magnetic field is doubled , what will be the magnetic force acting on the wire ?

A straight wire carrying a current of 12 A is bent into a semicircular arc of radius 2.0 cm as shown in figure (a). Consider the magnetic field vecB at the centre of the arc. (a) What is the magnetic field due to the straight segments ? (b) In what way the contribution to vecB from the semicircle differs from that of a circular loop and in what way does it resemble ? ( c) Would your answer be different if the wire were bent into a semicircular arc of the same radius but in the opposite way as shown in figure (b) ?

A straight horizontal conducting rod of length 0.45 m and mass 60 g is suspended by two vertical wires at its ends. A current of 5.0 A is set up in the rod through the wires. (a) What magnetic field should be set up normal to the conductor in order that the tension in the wires is zero? (b) What will be the total tension in the wires if the direction of current is reversed keeping the magnetic field same as before? (Ignore the mass of the wires.) g = 9.8 m s^(-2) .

A rectangular conducting loop consists of two wires on two opposite sides of length 1 joined together by rods of length d. The wires are each of the same material but with cross sections differing by a factor of 2. The thicker wire has a resistance R and the rods are of low resistance, which in turn are connected to a constant voltage source V_(0) . The loop is placed in uniform a magnetic field vecB at 45^(@) to its plane. Find the torque exerted by the magnetic field on the loop about an axis through the centres of rods.

(a) Obtain an expression for the mutual inductance between a long straight wire and a square loop of side a as shown in figure. (b) Now assume that the straight wire carries a current of 50 A and the loop is moved to the right with a constant velocity, v = 10 m/s. Calculate the induced emf in the loop at the instant when x = 0.2 m. Take a = 0.1 m and assume that the loop has a large resistance.