Moving Charges ...

Positive point chages $$q=+8.00\mu C$$ and $$q'=+3.00\mu C$$ are moving relative to an observer at point $$P$$, as shown in the figure. the distance $$d$$ is $$0.120$$ $$m$$. When the two charges are at the locations as shown in the figure, what are the magnitude and direction of the net magnetic field they produce at point $$P$$?
(Take $$v=4.50\times { 10 }^{ 6 }{ m{ s }^{ -1 }}$$ and $$v'=9.00\times { 10 }^{ 6 }{ m{ s }^{ -1 }}$$).

Figure shows an Amperian path $$ABCDA$$. Part $$ABC$$ is in verical plane $$PSTU$$ while part $$CDA$$ is in horizontal plane $$PQRS$$. Direction of circulation along the path is shown by an arrow near point $$B$$ and $$D$$.
$$\oint { \vec { B } .d\vec { l }  } $$ for this path according to Ampere's law will be :

A very long straight conducting wire lying along the z-axis carries a current of $$2A$$. The integral $$\oint { \vec { B } .d\vec { l }  } $$ is computed along the straight line $$PQ$$, where $$P$$ has the coordinates $$(2cm,0,0)$$ and $$Q$$ has the coordintes $$(2cm,2cm,0)$$. The integral has the magnitude (in SI units).

A conducting bar with mass m and length L slides over horizontal rails that are connected to a voltage source. The voltage source maintains a constant current I in the rails and bar, and a constant, uniform, vertical magnetic field $$\vec B$$ fills the region between the rails (as shown in fig). Find the magnitude and direction of the net force on the conducting bar. Ignore friction, air resistance and electrical resistance :

A magnetic field $$\vec B=B_0\hat j$$ exists in the region $$a < x < 2a$$ and $$\vec B=-B_0\hat j$$, in the region 2a < x < 3a, where $$V_0$$ is a positive constant. A positive point charge moving with a velocity $$\vec v=v_0\hat i$$, where $$v_0$$ is a positive constant, enters the magnetic field at $$x=a$$. The trajectory of the charge in this region can be like

Two long parallel wires are separated by a distance of $$2.50 cm$$.The force per unit length that each wire exerts on the other is $$4.00\times {10}^{-5}N/m$$, and the wires repel each other. The current in one wire is $$0.600 A$$. What is the current in the second wire?

Consider the three long,straight,parallel wires as shown in figure.Find the force experienced by a 25 cm length of wire C.

Three wires $$A,B$$, and $$C$$ all are all parallel and have the same magnitude of current. Wires $$A$$ and $$C$$ have current going toward the top of the screen while wire $$B$$ (which is in the middle) has current going toward the bottom of the screen.
What is the direction of the force on $$A$$ because of the other two wires?

$$AB$$ is a long wire carrying a current $${I}_{1}$$ and $$PQRS$$ is a rectangular loop carrying currect $${I}_{2}$$ (as shown in the figure)
which among the following statements are correct?
(a) Arm $$PQ$$ will get attracted to wire $$AB$$, and the arm $$RS$$ will get repelled from wire $$AB$$
(b) Arm $$PQ$$ will get repelled from wire $$AB$$ and arm $$RS$$ attracted to wire $$AB$$
(c) Forces on the arm $$PQ$$ and $$RS$$ will be unequal and opposite
(d) Forces on the arm $$PQ$$ and $$RS$$ will be zero

An electric current carrying conductor produces .......... field around it