Four charges are arranged at the corners of a square, as...

Four charges are arranged at the corners of a square, as depicted in the figure. Using the symmetry of the arrangement, determine the direction of the electric field at the center of the square due to the four charges at the corners, given that qa = qb = -3.1 ?C and qc = qd = 3.1 ?C . Calculate the magnitude of the electric field, in newtons per coulomb, at the center of the square (the location of q), given that the square is 3.5 cm on a side. |E| =

Transcript

00:01 Hi, as shown in this figure, 4 charges qa, b, qc and qd are arranged at the corners of a square having side each of measurement 0 .035 meters.

00:12 The charges are of values 3 .1 microculum charge a and b or negative fuel charged, charge c and d are positively charged.

00:21 Question is to determine the magnitude and direction of the net electric field at the center where a charge q is located.

00:28 The electric field due to these two negative charges will be acting towards its as by the nature and electric field due to charge c and d will be acting away from it since electric field, electric field, electric lines of force, charts from positive charge and terminates at negative charge.

00:45 The net electric field due to these two charges, ea and eb, will be acting upward.

00:51 Also, the net electric field resultant field due to ec and eed, they also acts upward.

00:57 Therefore, the resultant electric field, the net electric field, part a of the equation, the direction of the net electric field is above as shown here.

01:13 Part b is to determine its magnitude.

01:16 Magnitude of net electric field.

01:20 The x component of individual electric field, they get cancelled at each other, hence only the y components remaining.

01:30 Therefore net electric field can be written as ea cos 45 plus eb cost 45 plus ec cost 45 plus ed cost 45 as this angle is 45 degrees hence e net can be written as taking out cost 45 as a common term outside...

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