(a) an alpha particle ($$q=+2e, m = 4.0 u$$) and

(b) a deuteron ($$q=+e, m = 2.0 u$$) have if they are to circulate in the same circular path?

In a long, straight, vertical lightning stroke, electrons move downward and positive ions move upward and constitute a current of magnitude $$20.0 \,kA$$. At a location $$50.0 \,m$$ east of the middle of the stroke, a free electron drifts through the air toward the west with a speed of $$300 \,m/s$$.

(a) Make a sketch showing the various vectors involved. Ignore the effect of the Earths magnetic field.

(b) Find the vector force the lightning stroke exerts on the electron.

(c) Find the radius of the electron's path.

(d) Is it a good approximation to model the electron as moving in a uniform field? Explain your answer.

(e) If it does not collide with any obstacles, how many revolutions will the electron complete during the $$60.0-\mu s$$ duration of the lightning stroke?

The two wires shown in Figure are separated by $$d = 10.0 \,cm$$ and carry currents of $$I = 5.00 \,A$$ in opposite directions. Find the magnitude and direction of the net magnetic field

(a) at a point midway between the wires;

(b) at point $$P_1, \,10.0 \,cm$$ to the right of the wire on the right; and

(c) at point $$P_2, \,2d = 20.0 \,cm$$ to the left of the wire on the left.

Two long, parallel wires carry currents of $$I_1 = 3.00 \,A$$ and $$I_2 = 5.00 \,A$$ in the directions indicated in Figure.

(a) Find the magnitude and direction of the magnetic field at a point midway between the wires.

(b) Find the magnitude and direction of the magnetic field at point $$P$$, located $$d = 20.0 \,cm$$ above the wire carrying the $$5.00-A$$ current.

Three long, parallel conductors each carry a current of $$I = 2.00 A$$. Figure is an end view of the conductors, with each current coming out of the page. Taking $$a = 1.00 \,cm$$, determine the magnitude and direction of the magnetic field at

(a) point A,

(b) point B, and

(c) point C.

Two long, parallel wires are attracted to each other by a force per unit length of $$320 \mu \,N/m$$. One wire carries a current of $$20.0 \,A$$ to the right and is located along the line $$y = 0.500 \,m$$. The second wire lies along the x axis. Determine the value of $$y$$ for the line in the plane of the two wires along which the total magnetic field is zero.

A wire carrying a current $$I$$ is bent into the shape of an equilateral triangle of side $$L$$.

(a) Find the magnitude of the magnetic field at the center of the triangle.

(b) At a point halfway between the center and any vertex, is the field stronger or weaker than at the center?Give a qualitative argument for your answer.

Figure is a cross-sectional view of a coaxial cable. The center conductor is surrounded by a rubber layer, an outer conductor, and another rubber layer. In a particular application, the current in the inner conductor is $$I_1 = 1.00 \,A$$ out of the page and the current in the outer conductor is $$I_2 = 3.00 \,A$$ into the page. Assuming the distance $$d = 1.00 \,mm$$, determine the magnitude and direction of the magnetic field at

(a) point a and

(b) point b.

What is it necessary to introduce a cylindrical soft iron core inside the coil of a galvanometer?

$$F=\dfrac {\mu_0 I_1 I_2}{2\pi d} $$

Where $$I_1$$ and $$I_2$$ are the currents flowing through the two wires.

Use this expression, and the sign convention that the:

Force of attraction is assigned a negative sign and force of repulsion is assigned a positive sign.'

Draw graphs showing dependence of $$F$$ on

$$d$$ when the product $$I_1 I_2$$ is maintained at a constant positive value.

(b) What is the source of energy associated with the current obtained in part(a)?

Two parallel wires separated by $$4.00 \,cm$$ repel each other with a force per unit length of $$2.00 \times 10^{-4} \,N/m$$. The current in one wire is $$5.00 \,A$$.

(a) Find the current in the other wire.

(b) Are the currents in the same direction or in opposite directions?

(c) What would happen if the direction of one current were reversed and doubled?

(a) $$1/\pi $$

(b) $$\pi /2$$

Identify the device shown in the figure.

An electron moving horizontally with a velocity of $$4\times 10^4\ m/s$$ enters a region of uniform magnetic field of $$10^{-5}\ T$$ acting vertically downward as shown in the figure.

Draw its trajectory and find out the time it takes to come out of the region of magnetic field.

Two long, parallel conductors, separated by $$10.0 \,cm$$, carry currents in the same direction. The first wire carries a current $$I_1 = 5.00 \,A$$, and the second carries $$I_2 =8.00 \,A$$.

(a) What is the magnitude of the magnetic field created by $$I_1$$ at the location of $$I_2$$?

(b) What is the force per unit length exerted by $$I_1$$ on $$I_2$$?

(c) What is the magnitude of the magnetic field created by $$I_2$$ at the location of $$I_1$$?

(d) What is the force per length exerted by $$I_2$$ on $$I_1$$?

$$ dB^{\rightarrow}= \dfrac{\mu o}{4\pi}$$ $$\dfrac{idl^{\rightarrow }\times r^{\rightarrow }}{ | r |^{3}}$$

(a) What is the amount of work required by an external torque to turn the magnet so as to align its magnetic moment: (i) normal to the field direction, (ii) opposite to the field direction?

(b) What is the torque on the magnet in cases (i) and (ii)?

If the charge on the croquet ball is 1.0 C, how much force acts on the croquet ball due to the magnetic field and in what direction?

(b) An observer to the left of a solenoid of N terms each of cross section area A observes that a steady current I in it flows in the clockwise direction. Depict the magnetic field lines due to the solenoid specifying its polarity and show that it acts as a bar magnet of magnetic momentum $$m = NIA$$

Write the path of motion of an electron when it enters in magnetic field at

(a) perpendicular

(b) an angle $$\theta$$.

(b) State Ampere's circuital law. Using the law, obtain an expression for the magnetic field well aside the solenoid of finite length.

(c) Which configuration corresponds to the lowest potential energy among all the configurations shown?

(i) time period of revolution

(ii) kinetic energy of the particle

What is the amount of work required by an external torque to turn the magnet so as to align its magnetic moment: (i) normal to the field direction, (ii) opposite to the field direction?

column I | Column II | ||

(A) | Equilibrium of loop | (p) | Along z-axis |

(B) | torque of the loop | (q) | Zero |

(C) | Magnetic moment of the loop | (r) | Stable |

(D) | Potential energy of loop | (s) | None of the above |

A circular coil of $$300 $$ turns and diameter $$14 cm$$ carries a current of $$15 A$$. Calculate the magnitude of the magnetic dipole moment associated with the coil.

possible values of $$\mu_{orb,z}$$?

momentum with $$m=0$$, what are the components (a) $$L_{orb,z}$$, and

(b) $$\mu_{orb,z}$$? If the atom is in an external magnetic field that has a magnitude $$35\, mT$$, and is directed along the z-axis, what are (c) the

energy $$U_{orb}$$ associated with and (d) the energy $$U_{spin}$$ associated

with $$\vec \mu_s$$? If, instead, the electron has, what are (e) $$L_{orb,z}$$,

(f)$$\mu_{orb,z}$$, (g)$$U_{orb}$$, and (h)$$U_{spin}$$?

Write the expression for the force $$\vec F$$ acting on a particle of mass $$m$$ and charge $$q$$ moving with velocity $$\vec V$$ in a magnetic field $$\vec B$$ Under what conditions will it move in a circular path?

Draw the magnetic field lines due to two straight, long, parallel conductors carrying currents $$I_1$$ and $$I_2$$ in the same direction. Write an expression for the force acting per unit length on one conductor due to other. Is this force attractive or repulsive?

Show that the kinetic energy of the particle moving in magnetic field remains constant.

(i) pushed into the coil with its north pole entering first

(ii) held at rest inside the coil

(iii) pulled out again?

(b) Name the phenomenon

(b) the minimum frequency of the cyclotron's oscillator at which the kinetic energy of the protons amounts to $$T = 20\ MeV$$ by the end of acceleration.

(a) Fig. a, with curvature radius $$R = 10\ cm$$;

(b) Fig. b, the distance between the long parallel segments of the wire being equal to $$l = 20\ cm$$.

Calculate the magnitude of the magnetic field at a point $$25.0 \,cm$$ from a long, thin conductor carrying a current of $$2.00 \,A$$.

A proton moving in the plane of the page has a kinetic energy of $$6.00 \,MeV$$. A magnetic field of magnitude $$B = 1.00 \,T$$ is directed into the page. The proton enters the magnetic field with its velocity vector at an angle $$\theta = 45.0^{o}$$ to the linear boundary of the field as shown in Figure.

(a) Find $$x$$, the distance from the point of entry to where the proton will leave the field.

(b) Determine $$\theta$$, the angle between the boundary and the proton's velocity vector as it leaves the field.

Given that , i = 4.0 A, OA=20 cm and AB =10 cm.

Masses of coils are $$M$$ and $$m$$, respectively.

Hence derive the expression for the magnetic field due to a current carrying loop of radius $$R$$ at a point P distant $$x$$ from its centre along the axis of the loop.

(b) Explain how Biot - Savart law enables one to express the Ampere's circuital law in the integral form, viz.,

$$\vec B . \vec {dl} = \mu_o I$$

where $$I$$ is the total current passing through the surface.

One long wire carries current $$30.0 \,A$$ to the left along the x axis. A second long wire carries current $$50.0 \,A$$ to the right along the line $$(y = 0.280 \,m, z = 0)$$.

(a) Where in the plane of the two wires is the total magnetic field equal to zero?

(b) A particle with a charge of $$-2.00 \,\mu C$$ is moving with a velocity of $$150\hat{i} \,Mm/s$$ along the line $$(y = 0.100 \,m, z = 0)$$. Calculate the vector magnetic force acting on the particle.

(c) What If? A uniform electric field is applied to allow this particle to pass through this region undeflected. Calculate the required vector electric field.

(a) the electrons speed,

(b) the magnetic field magnitude,

(c) the circling frequency, and

(d) the period of the motion.

(a) its speed,

(b) its period of revolution,

(c) its kinetic energy, and

(d) the potential difference through which it would have to be accelerated to achieve this energy.

(a) the protons speed and

(b) its kinetic energy in electron-volts.

(a) What magnitude $$B$$ of magnetic field is required to achieve resonance?

(b) At that field magnitude, what is the kinetic energy of a proton emerging from the cyclotron?

Determine the magnetic field (in terms of $$I, \,a$$, and $$d$$ ) at the origin due to the current loop in Figure. The loop extends to infinity above the figure.

equally long plastic cylinder, at radius R=20.0 cm from the cylinder’s central axis. Figure (a) shows, in cross section, the cylinder

and wire 1 but not wire 2.With wire 2 fixed in place, wire 1 is moved around the cylinder, from angle $$\theta_{1}=0^{\circ}$$ to angle $$\theta_{1}=180^{\circ}$$, through the first and second quadrants of the $$xy$$ coordinate system. The net magnetic filed $$\vec{B}$$ at the center of the cylinder is measures as the function of $$\theta_{1}$$. Figure(b) gives the $$x$$ component $$B_{x}$$ of that field as a function of $$\theta_{1}$$ (the vertical scale is set by $$B_{xx}=6.0\hspace{0.05cm} \mu T)$$ and figure (c) gives the $$y$$ componenet of $$B_{y}$$ (the vertical scale is set by $$B_{yx}=4.0 \mu T$$ (a)At what angle $$\theta_{2}$$ is wire located? What are the (b) size and (c) direction (into or out of the page) of the current in wire 1 and the (d) size and (e) direction of the current in wire 2?

magnetic field $$\vec{B}$$, goes through half a circle, and then exits that region. The particle is either a proton or an electron (you must decide which). It spends $$130 ns$$ in the region.

(a) What is the magnitude of $$\vec{B}$$?

(b) If the particle is sent back through the magnetic field (along the same initial path) but with $$2.00$$ times its previous kinetic energy, how much time does it spend in the field during this trip?

5.00 A$$. The sides of the loop are parallel to the coordinate axes shown, with $$AB = 20.0 cm$$,$$BC = 30.0 cm$$, and $$FA = 10.0 cm$$. In unit-vector notation, what is the magnetic dipole moment of this loop? (Hint: Imagine equal and opposite currents $$i$$ in the line segment $$AD$$; then treat the two rectangular loops ABCDA and ADEFA.)

Find out the expression for the distance moved by the particle along the magnetic field in one rotation.

Force with which it strikes a target on the screen. if the proton beam current is equal to $$0.80\ mA$$.

density $$u_B$$ set up by the two currents at the origin. Figure b gives $$u_B$$ as a function of the position x of wireThe curve has an symptote of $$u_b=1.96nJ/m^3$$ as $$x \rightarrow \infty $$, and the horizontal axis scale is set by $$x_s60.0cm$$.What is the value of (a) $$i_1$$ and (b) $$i_2$$?

If $$B$$ is independent of time, obtain $$v(t)$$, assuming $$v(0) = u_{0}$$, show that the decrease in kinetic energy of $$XY$$ equals the heat lost in $$R$$.

(Proton mass $$= 1.67 \times 10^{-27} kg, e = 1.60 \times 10^{-19}C, eV = 1.6 \times 10^{-19}J$$)