Chapter 4: Moving Charges and Magnetism

A multirange voltmeter can be constructed by using a galvanometer circuit, as shown in the figure. We want to construct a voltmeter that can measure 2V, 20V, and 200V using a galvanometer of resistance 10Ω and that produces maximum deflection for a current of 1 mA. Find R1, R2, and R3 that have to be used.

A long straight wire carrying a current of 25 A rests on a table, as shown in the figure. Another wire PQ of length 1 m, mass 2.5 g carries the same current but in the opposite direction. The wire PQ is free to slide up and down. To what height will PQ rise?

A 100-turn rectangular coil ABCD is hung from one arm of a balance. A mass of 500 g is added to the other arm to balance the weight of the coil. A current 4.9 A passes through the coil, and a constant magnetic field of 0.2 T acting inward is switched on such that only arm CD of length 1 cm lies in the field. How much additional mass ‘m’ must be added to regain the balance?

A rectangular conducting loop consists of two wires on two opposite sides of length l 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 Vo. The loop is placed in uniform a magnetic field B at 45o to its plane. Find τ, the torque exerted by the magnetic field on the loop about an axis through the centres of rods.

An electron and a positron are released from (0, 0, 0) and (0, 0, 1.5R), respectively, in a uniform magnetic field
each with an equal momentum of magnitude p = eBR. Under what conditions on the direction of momentum will the orbits be non-intersecting circles?

A uniform conducting wire of length 12a and resistance R is wound up as a current-carrying coil in the shape of i) an equilateral triangle of side a, ii) a square of sides a, and iii) a regular hexagon of sides a. The coil is connected to a voltage source V0. Find the magnetic moment of the coils in each case.

Consider a circular current-carrying loop of radius R in the x-y plane with the centre at the origin. Consider the line integral
taken along the z-axis.

a) show that
monotonically increases with L

b) use an appropriate Amperian loop to that
where I is the current in the wire

c) verify directly the above result

d) suppose we replace the circular coil with a square coil of sides R carrying the same current I. What can you say about

A multirange current meter can be constructed by using a galvanometer circuit shown in the figure. We want a current meter that can measure 10 mA, 100 mA, and 1 A using a galvanometer of resistance 10Ω and that produces maximum deflection for a current of 1 mA. Find S1, S2, and S3 that have to be used.

Five long wires A, B, C, D, and E, each carrying I are arranged to form the edges of a pentagonal prism, as shown in the figure. Each carries current out of the plane of the paper.

a) what will be magnetic induction at a point on the axis O> Axis is at a distance R from each wire

b) what will be the field if the current in one of the wires is switched off

c) what if the current in one of the wires A is reversed