Problem 9: Four charges are arranged at the corners of a...

Problem 9: Four charges are arranged at the corners of a square, as depicted in the figure. Part (a) 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 = -4.6 ?C and qc = qd = 4.6 ?C . Part (b) 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 5.5 cm on a side.

Transcript

00:02 Hi, here in this given problem there is a square shaped arrangement of the four charges.

00:14 And the charges are named as qa, qb, and then qc and at last qd.

00:27 We assume these vertices of the square also to be represented as a and b and c and d.

00:43 Then we can represent center of the square also.

00:55 This is the center of the square.

00:58 Now these charges are given as qa is equal to.

01:04 Qb, these two charges are identical minus 4 .6 microculam each and qc that is equal to qd.

01:18 And these are 4 .6 microculum each.

01:23 In the first part of the problem, we have to find the direction of net electric field.

01:31 As this is a negative charge, this is also negative charge, this is positive and this one is also positive and we know electric field goes away from a positive charge and approaches a negative charge so electric field due to electric fields due to qa and qb will be towards a and b respectively, means if we show these two electric fields, this will be qa, this will be ea, this will be e b, both towards the negative charges.

03:06 And similarly as the electric field goes away from the positive charge, so due to this qc it will be going away, means it will be along this e b, so this is e .c.

03:18 And here it will be due to qd.

03:22 Let it represent like ed.

03:26 So we can note it down here also.

03:32 And due to qc and qd also these will be along the same directions as it is clear from the figure.

04:09 So, and one more thing as all the charges are having same magnitude and same distance from the observation point, observation point means center of the square.

04:55 So using an expression for electric field that is k, electrostatic constant k into q by r square as k and q and r all the things are same all these electric fields will be equal in magnitude means e a will be equal to e b will be equal to e c and that is equal to e d now we will consider the sum of these two electric fields e a and ed to be given as e one and the sum of these two e2.

05:39 So, e1 that will be equal to ea plus e d and e2 that will be equal to e b plus e c...

Question

Please give Ace some feedback