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Magnetic effects of Current: Field, force, induction

1) The figure (*see attachment) shows 11 paths through a region of uniform magnetic field. One path is a straight line; the rest are half circles. The table (*see attachment) gives the masses, charges and speeds of the 11 particles that take these paths through the field in the direction shown. Which path corresponds to which particle in the table?

2) The following table (*see attachment) gives the number of turns per unit length, n, and the current, I, through six ideal solenoids of different radii. You want to combine them concentrically to produce a net magnetic field of zero along the central axis. Can this be done with (a) two of them, (b) three of them, (c) four of them, (d) five of them, (e) six of them? If so answer by listing which solenoids are to be used and indicate the direction of the currents.

3) Two long parallel wires which are separated by a distance of 18 cm, carry currents of 7A and 8A. (a) Where is the net magnetic field zero? (i.e. how many cm from the midpoint between the two wires is the magnetic field=zero?) (b) what is the B-field at a point 5cm to the left of wire 1 and 5cm below both wires?

4) In the figure (*see attached), E = 100 V, R1 = 20 ohms, R3 = 30 ohms and L = 2 H. Find the values of I1 and I2 (a) immediately after closing the switch S, (b) a long time after switch S is closed, (c) immediately after switch S is opened and (d) a long time after switch S is opened.


Solution Preview

Solution 1:
The radius of the circular path traced by a charged particle in a uniform magnetic field is given by (magnitude) R = mv/bq and the direction of rotation can be determined by using Fleming's left hand rule. The direction will be opposite if the either the charge is negative or the direction of the velocity is reversed.
Let the radius in this problem mv/Bq = r then the radii of the paths of different particles are given as
Particle 1 ; 2 ; 3 ; 4 ; 5 ; 6 ; 7 ; 8 ; 9 ; 10 ; 11

Radius 2r ; r/2 ; r ; 8r ; 4r ; (-)2r ; (-)r/4; (-)r ; (-8)r ; (-4)r ; inf.

The smallest radius is r/4 for the charge no. 7 (which is for path d in fig.) which is having a negative charge and the direction ...

Solution Summary

Force problems related to magnetic effect of electric current are solved

-------1. Path of a charged particle in a magnetic field.
------- 2. Field due to number of solenoids.
------- 3. field due to two long parallel wires carrying current.
--------4. growth of current in an inductor