Physics Answer Note #61

Question 1 What is the degree of deflection and direction of protons in an electric field Answer The degree of deflection and direction of protons in an electric field is determined by the strength and direction of the electric field, as well as the charge and mass of the proton. When a proton enters an electric field, it will experience a force that is perpendicular to its velocity and the electric field. This force causes the proton to move in a curved path, resulting in deflection. The direction of deflection of the proton will depend on its initial velocity and the direction of the electric field. If the proton is moving in the same direction as the electric field, it will experience a force in the opposite direction, causing it to curve towards the negative terminal of the electric field. If the proton is moving in the opposite direction of the electric field, it will experience a force in the same direction, causing it to curve towards the positive terminal of the electric field. The degree of deflection will depend on the strength of the electric field and the initial velocity of the proton. To calculate the degree of deflection, we can use the formula F = qE, where F is the force, q is the charge of the proton, and E is the strength of the electric field. We can also use the formula F = ma, where m is the mass of the proton and a is the acceleration due to the electric field. Combining these two equations, we can calculate the acceleration of the proton and then use kinematic equations to determine the degree of deflection. Question 2 why is an electron strongly attracted to the positive plate Answer "Why is an electron strongly attracted to the positive plate?" Electrons are subatomic particles that have a negative charge and are located within the atom's orbitals. In terms of electrostatics, opposites attract. This means that a positively charged plate will strongly attract a negatively charged electron. One reason for this attraction is due to the concept of electric potential energy. Electric potential energy is the energy possessed by a charged particle due to its position in an electric field. As an electron moves closer to a positively charged plate, its potential energy decreases. According to Coulomb's law, the force of attraction between two charged particles is directly proportional to the magnitude of the charges and inversely proportional to the square of the distance between them. Since the distance between the electron and positive plate decreases, the force of attraction between them increases. Furthermore, electrons are held in place by the positive charge of protons in the nucleus of an atom. This force of attraction between the positive nucleus and negative electrons is what keeps the atom intact. When an electron is removed from an atom, it creates a positively charged ion. This imbalance of charges, with one positively charged ion and one negatively charged electron, creates a strong force of attraction between the two. In addition, the positive plate acts as a source of an electric field due to its charge. This electric field exerts a force on the electron, pulling it towards the positive plate. As the electron gets closer to the positive plate, the strength of the electric field increases, resulting in a stronger force of attraction. In summary, an electron is strongly attracted to a positive plate due to the decrease in potential energy, the force of attraction between positive ions and negative electrons, and the electric field created by the positive plate itself. This strong attraction is fundamental to understanding the behavior of charged particles in electrostatics. Question 3 Explain the direction and degree of deflection of protons, electrons and neutrons in an electric field. Answer In an electric field, charged particles such as protons, electrons, and neutrons experience a force that causes them to move. This movement, also known as deflection, is directly influenced by the electric field strength and direction. The strength of the electric field is measured by the electric field intensity, which is the amount of force exerted on a unit of charge at a specific point in the field. The electric field intensity is calculated using the following formula: E = F/q Where E is the electric field intensity, F is the force exerted on the charge, and q is the magnitude of the charge. The direction of the electric field is determined by the direction of the force acting on a positive test charge. This means that in a region of the electric field, a positive charge will experience a force in the direction of the electric field, while a negative charge will experience a force in the opposite direction. Protons, being positively charged particles, will experience a force in the direction of the electric field. This means that in an electric field pointing towards the right, protons will be deflected towards the right. The degree of deflection of protons will depend on the strength of the electric field and the magnitude of the charge on the proton. On the other hand, electrons, being negatively charged, will be deflected in the opposite direction to the electric field. In the case of an electric field pointing towards the right, electrons will be deflected towards the left. The degree of deflection of electrons will also depend on the strength of the electric field and the magnitude of the charge on the electron. It is important to note that neutrons do not have a charge and therefore do not experience a force in an electric field. This is because the force acting on a charge in an electric field is given by the formula F = qE, where q is the charge of the particle. As neutrons have a charge of 0, the force exerted on them is also 0, resulting in no deflection. Question 4 In Fig. 21-25, particle 1 of charge +1.0 µC and particle 2 00 of charge 3.0 µC are held at separa- tion L = 10.0 cm on an x axis. If particle 3 of unknown charge q3 is to be located such that the net electrostatic force on it from particles 1 and 2 is zero, what must be the (a) x and (b) y coordinates of particle 3? Answer To determine the coordinates for particle 3, we first need to understand the concept of electrostatic forces and Coulomb's law. According to Coulomb's law, the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. In this specific scenario, the net electrostatic force on particle 3 from particles 1 and 2 must be zero. This means that the forces from both particles must cancel each other out, resulting in a net force of zero. To achieve this, we need to place particle 3 at a specific location where the forces from particles 1 and 2 acting on it are equal in magnitude but opposite in direction. (a) To determine the x-coordinate of particle 3, we can use the equation for electrostatic force: F = kq1q2/r^2, where k is the Coulomb's constant, q1 and q2 are the charges of particles 1 and 2 respectively, and r is the distance between them. Since the net force on particle 3 must be zero, we can set up the following equation: F1 + F2 = 0 k(q1q3)/(x^2) + k(q2q3)/((L-x)^2) = 0 Solving for x, we get x = L(q2/(q1+q2)) = 10 cm (3 µC/(1 µC + 3 µC)) = 7.5 cm Therefore, the x-coordinate for particle 3 is 7.5 cm. (b) To determine the y-coordinate of particle 3, we need to consider the direction of the forces from particles 1 and 2. Since the forces are in opposite directions, we can place particle 3 at any point on the y-axis and still achieve a net force of zero. Therefore, the ycoordinate for particle 3 can be any value. Question 5 , particle 1 of charge +1.0 µC and particle 2 00 of charge 3.0 µC are held at separa- tion L = 10.0 cm on an x axis. If particle 3 of unknown charge q3 is to be located such that the net electrostatic force on it from particles 1 and 2 is zero, what must be the (a) x and (b) y coordinates of particle 3? Answer According to Coulomb's Law, the electric force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. In this scenario, we have two particles, particle 1 with a charge of +1.0 µC and particle 2 with a charge of +3.0 µC, held at a separation of 10.0 cm on the x-axis. We are asked to find the coordinates of particle 3, with an unknown charge q3, where the net electrostatic force from particles 1 and 2 is zero. To find the coordinates of particle 3, we can use the principle of superposition to find the net force on the particle 3 due to particle 1 and particle 2 separately, and then set it equal to zero to find the coordinates. Let's first consider the force on particle 3 from particle 1. According to Coulomb's Law, the magnitude of the force, F13, can be calculated as: F13 = k * (q3 * q1) / r13^2 where k is the electrostatic constant (9*10^9 Nm^2/C^2), q1 and q3 are the charges of particles 1 and 3 respectively, and r13 is the distance between them. Similarly, the force on particle 3 from particle 2, F23, can be calculated as: F23 = k * (q3 * q2) / r23^2 where q2 is the charge of particle 2 and r23 is the distance between particle 3 and 2. To find the coordinates of particle 3, we must set the net force equal to 0, i.e. F13 + F23 = 0. Solving for q3, we get: q3 = -q2 * r23^2 / r13^2 (1) Next, we can use the Pythagorean theorem to calculate r13 and r23: r13 = sqrt[(x - 10)^2 + y^2] and r23 = sqrt[x^2 + y^2] Putting these values into equation (1), we get: q3 = -q2 * [x^2 + y^2] / [(x - 10)^2 + y^2] (2) To find the coordinates of particle 3, we need to solve for x and y. We can do this by using the method of substitution. From equation (2), we get: q3 = -q2 * (x^2 + y^2) / [(x - 10)^2 + y^2] Solving for x, we get: x = sqrt[10 * (q2 * y^2 + q3 * y^2) / (q2 - q3)] (3) Similarly, solving for y, we get: y = sqrt[10 * (q2 * x^2 + q3 * x^2) / (q2 - q3)] (4) Equations (3) and (4) give us the coordinates of particle 3 in terms of the unknown charge q3. In conclusion, to find the coordinates of particle 3 so that the net electrostatic force on it from particles 1 and 2 is zero, we can use the equations derived from Coulomb's Law, (3) and (4), where q3 is the unknown charge. It is important to note that these equations apply only when the charges are held on the x-axis at a distance of 10.0 cm.