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1.	A wide copper strip of width l is bent into piece of slendder tubing of radius R with two plane extension as shown (Fig. 1.12). A current I flows through the strip, distributed uniformly over its width. Ib this way, one-turn solenoid has been formed (a) Derive an expression for the magnetic field in the tubular part.
Answer» Correct Answer - `(mu_(0)i)/(l)`

2.	What pressure does the lateral surface of a long straight solenoid with n turns per unit length experience when a current I flows through it.
Answer» Correct Answer - `p=(1)/(2)mu_(0)n^(2)I^(2)`

3.	A current `I` flows in a long single layer solenoid with cross-sectional radius `R`. The number of turns per unit length of the solenoid equals `n`. Find the limiting current at which the winding may ruputure if the tensile strength of the wire is equal to `F_(l i m)`.
Answer» Correct Answer - `I=sqrt((2sigma)/(mu_(0)nR))`

4.	A current `I` flows in a long thin walled cylinder of radius `R`. What pressure do the walls of the cylinder experience ?
Answer» Correct Answer - `p=(mu_(0)I^(2))/(8pi^(2)R^(2))`

5.	A unifrom current of density `f` flows inside an infinite plate of thickness `2d` parallel to its surface . Find the magentic induction induced by this current as a funcition of the distance `x` from the median palane of the plate. The magnitude permeability is assumed to be equal to unity both inside and outside the plates.
Answer» Correct Answer - `B=mu_(0)jx("inside")and B=mu_(0)jd("outside")`

6.	A this disc of dielectric material, with a total charge +q distributed uniformly over its surface, rotates with angular speed `omega` about an axis perpendicular to the disc and passing through its centre .Find the magnetic moment with its angular momentum , assuming that its mass is m. [Hint : Consider a ring of radius x and thickness dx. Calculate charge on it and then the current consituited by its rotation .Find its magnetic moment and integrate for the whole disc.]
Answer» Correct Answer - `(1)/(4)qwr^(2),(q)/(2m)`

7.	Electric charge +q is iniformaly distributed over the entire volume of a sphere of radius r. Calculate the magnetic moment of the sphere if it spins about its diameter with angular speed `omega` . Compare this moment with its angular momentum, assuming that its mass is m.
Answer» Correct Answer - `(1)/(5)qwr^(2),(q)/(2m)`

8.	A ring of dielectric material, with a total charge +q distributed uniformly over its surface, rotates with angular speed `omega.` Find the magnetic moment of the ring .Compare its magnetic moment with its angular momentum , assuming that its mass is m.
Answer» Correct Answer - `(1)/(2)qwr^(2),)(q)/(2m)`

9.	Two currrent elements `2 xx 10^(-4)` A m and `5 xx 10^(-4)` Am are placed at the vertices A and B of an equilateral triangle along AB in the same sense. Calculate the magnetic field at C. (Each side of the triangle measures 10 cm)
Answer» Correct Answer - `6.06 xx 10^(-2) T`

10.	A long cylindrical conductor of radius a contains a long cylindrical holr of radius l. The axes of the two cylinders are parallel and are at a distance d apart. A current I is uniformly distributed over the cross-section. Find the magnetic field at the centre of the hole. [Hint: Apply the principle of superposition of magnetic field]
Answer» Correct Answer - `(mu_(0)id)/(2pi(a^(2)-b^(2))`

11.	The current density `bar(J)` inside a long, solid cylindrical wire of radius `a = 12 mm` is in the direction of the central axis, and its magnitude varies linearly with radial distance r from the axis according to `J = (J_(0) r)/(a)`, where `J_(0) = (10^(5))/(4 pi) A//m^(2)`. Find the magnitude of the magnetic field at `r = (a)/(2)` in `mu T`
Answer» Correct Answer - `(mu_(0)i)/(2pia^(3))r^(2)`

12.	A current elemetns of 0.2 A m is fixed at the centre of a circle of radius 10 cm . Another element of strength 0.5 A m is placed along the circumference and moved round the circle. At which positions will they sent maximum force on each other? Calculate these forces.
Answer» Correct Answer - `10^(-6)` (maximum) when they are parallel and 0 (minimum) when they are perpendicular

13.	An electron of velocity `2 xx 10^(6) m s^(-1)` is moving in magneitc field of strength 1 T making an angle `45^(@)` with it. Find the magnitude and direction of the magnetic force experienced by it. Charge of electron`=1.6 xx 10^(-19)` C. [ Hint : `vec F=q_(0)vec vxx vec B`.]
Answer» Correct Answer - `2.26 xx 10^(-13)N`

14.	The plane of a rectangular coil of wire of dimensions `0.05 xx 0.10m` and carrying a current of 10 A ,is parallel to a magnetic field of 0.1 T . What is the torque on the coil? What will be the torque when the normal to the coil makes an angle of `30^(@)` with the direction of the field ?
Answer» Correct Answer - `5 xx 10^(-13) N m; 2.5 xx 10^(-3) N m`