need help with 6 and 7 please thanks LOR. Be on your answers to the previous par

Question

need help with 6 and 7 please thanks

LOR. Be on your answers to the previous parts, which force or forces (electric, magnetic and gravitational) contributes signifi. cantly to this inward force? 6 Suppose a charged particle is moving through a region of space in which there is an electric field perpendicular to its velocity vector, and also a magnetic field perpendicular to both the particle's velocity vector and the electric field. Show that there will be one particular velocity at which the particle can be moving that results in a total force of zero on it; this requires that you analyze both the magnitudes and the directions of the forces compared to one another. Relate this velocity to the magnitudes of the electric and magnetic fields. (Such an arrangement, called a velocity filter, is one way of determining the speed of an unknown particle.) 7 If you put four times more current through a solenoid, how many times more energy is stored in its magnetic field? 8 Suppose we are given a permanent magnet with a complicated, asymmetric shape. Describe how a series of measurements with uld be used to determine the

Explanation / Answer

6)Let v be the velocity of the particle, B and E be the magnetic and electric field respectively. q be the charge on the particle.

We know that the electric force on a charged particle is:

Fe = q E

the mangetic force on the particle is;

Fm = q v B

The above two forces balances each other and the total force is zero.

Fm = Fe

q v B = q E

q gets cancelled ; v B = E

v = E/B

Hence, v = E/B

7)The stored energy in a solenoid is given by:

U = 1/2 L I^2

I' = 4 I

U' = 1/2 L (4I)^2 = 1/2 L (16 I^2)

U'/U = 1/2 L 16 I^2 / (1/2 L I^2) = 16

Hence, U' = 16 U

So when the current is increased by four times, the energy gets increased by 16 times, as it varies with the square of current.

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