Fieldlines zero electric potential1/7/2024 well, in both cases the work done is the same. i.e., non-zero.Īnswer : The electron is traveling considerably faster than the proton. However, the algebraic sum of the potentials is 2kQ/r. Let's look at an exampleĪt the midpoint beween two identical charges, P, the resultant electric field is zero. By definition, E = -dV/dx, therefore, if E = 0, V is constant, but not necessarily zero. So, the electric field and the potential will both be zero if Q 1 and Q 3 have the same sign and Q 2 and Q 4 have the same sign, which is opposite to the signs of Q 1 and Q 3.Īnswer : No, the fact that E = 0 does not mean that V = 0. This will occur if the two pairs have opposite signs. So, for a zero total potential, the potential of one diagonal pair must cancel the potential of the other diagonal pair. If a diagonal pair of charges has the same magnitude and sign they produce a non-zero potential. Therefore, the total electric field at the center will be zero if each diagonal pair of charges has the same magnitude and sign. So, if two diagonal charges have the same magnitude and sign then the electric fields due to these charges have equal magnitude but opposite directions and their resultant is zero. Q 2 and Q 3 are positive: V = -kQ/L + (kQ/L)cos45° + kQ/L = 0.707kQ/L.Īnswer : The electric field is the vector sum of the individual electric fields at the center the potential is the algebraic sum of the individual potentials at the center.Since we have to take the sum of the individual potentials we have: So, the two charges must be placed on diagonally opposite corners.Īnswer : Actually, it doesn't matter how you arrange the charges, the potential at the vacant corner is always positive!Īssume that the charges have magnitude Q. For the potentials on both vacant corners to be the same the distances have to be the same, Where r 1 and r 2 are the distances from charges Q 1 and Q 2 to a vacant corner, respectively. ![]() Since the potential of a point charge is given by kQ/r, and the charges are opposite in sign, the potential due to the two charges You should keep in mind that the zero has no significance and is only a matter of convenience in calculation.Answer : The potential at an "open" corner is simply the (algebraic) sum of the potentials at that point due to the individual charges. As a matter of convenience, you could set one end to be 0 so that the readout on the other end corresponds to the length of pen. All that matters is the difference between the measurements at the end points. Hence the measurements 0 and 5 is equivalent to 3 and 8, 4.65 and 9.65 and so on. ![]() When you measure it with the help of a ruler, it doesn't matter if one end of the pen coincides with the zero of the ruler or not. ![]() Let the length of the pen be 5 inches, say. Imagine you're trying to measure the length of a pen. I'll provide a cruder analogy, but this should help you understand what I've told in the previous paragraph. It is only the gradient of V that matters for the electric field. Now you see that the specification of the value of V is completely up to you. There is no mention of what $V$ value is at the two points. The electric field in terms of the potential is $\vec$.
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