Consider two separate systems, each with four charges of magnitude q arranged in

Question

Consider two separate systems, each with four charges of magnitude q arranged in a square of length L as shown above. Points a and c arc in the center of their squares while points b and d arc half way between the lower two charges. Select true or false for each statement. True: The electric potential at c is zero. False: The electric field at b is zero. True: The electric potential at a is zero. True: The electric potential at b is zero. False: The electric field at d is zero. False: The electric potential at d is zero. True: The electric field at a is zero. False: The electric field at c is zero. Using the diagram above, find the magnitude of the electric field at point d. DATA: q = 0.850 uC, L= 0.40 m. To get the y-component of E-field from a charge, calculate the magnitude of E with Coulombs law, then multiply by the cosine of the angle between the E-field and the y-axis. The cosine of an angle in a right triangle is the adjacent over the hypotenuse.

Explanation / Answer

electric field due to two positive charges will be 0 as they will cancel each other

electric field due to negative charge will be

E = k * q / distance^2

E = 9 * 10^9 * 0.85 * 10^-6 / sqrt(0.4^2 + 0.2^2)

E = 17105.92 N/C

this is the electric field due to one negative charge

electric field due to another negative charge will be same as magnitude of charge and distance are same

x component of electric field due to both the negative charges will cancel each other as it'll have equal magnitude but in opposite direction

y component of the electric field will add up

y component of the electric field = E * cos(30) + E * cos(30)

y component of the electric field = 2 * E * cos(30)

y component of the electric field = 2 * 17105.92 * cos(30)

y component of the electric field = 29628.3226 N/C

electric field at point d = 29628.3226 N/C

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