Suppose that a region of space contains uniform electric and magnetic fields of

Question

Suppose that a region of space contains uniform electric and magnetic fields of unknown direction and magnitude. In order to measure these fields, a test charge of Q = 10^-6 C is used. (In practice, there are much better ways to measure the fields, but we want to illustrate how the basic definitions work.) The following measurements are made: At rest, the test charge experiences a force of F_1 = 10 times 10^-5 N in the positive y-direction. Moving at a speed of v = 20 m/s in the positive y-direction, the charge experiences a force given by F_2vector = (10jcap - 2kcap) times 10^-5N. If the charge moves with the same speed in the positive z-direction, the force is F_3vector = (-icap + 12jcap) times 10^-5N. Use this information to find the electric and magnetic fields.

Explanation / Answer

Here,   Force due to Electric field =   qE

=>    10 * 10-5 j = 10-6 * E

=>    Electric field, E =   100 j   N/C

Here,   F2 = q (E + v X B)

   =>   ( 10 j - 2 k) * 10-5   =   10-6 * ( 100 j + 20 j X B )

=>        B = i + y j

Also, ( -i + 12 j) * 10   =   ( 100 j + 20 k X B )

=>     B =   (i + 0.5 j) T

=>   Electric field =    100 j   N/C

=>   Magnetic field =   ( i + 0.5 j ) T

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