Make a test for grade 12 physics with combinations of units, like questions with springs, energy, forces, circular motion, electric and magnetic fields into one question. Every que... Make a test for grade 12 physics with combinations of units, like questions with springs, energy, forces, circular motion, electric and magnetic fields into one question. Every question has about 2 or 3 units. Read more

Create a question where a charged particle moving in a magnetic field also involves a spring, combining units on forces, energy, and motion.

Here is an example question for Grade 12 Physics that combines multiple units:

Question: A charged particle with mass m and charge q enters a region with a uniform magnetic field B. The magnetic field is oriented perpendicular to the plane of motion, and the particle moves in a circular path with radius r. Additionally, the particle is attached to a spring with spring constant k and uncompressed length l. As the particle moves in its circular path, the spring stretches to a length 2l due to the centripetal force required to maintain the circular motion.

1. Determine the speed of the particle in terms of m, q, B, and other constants.
2. Calculate the amount of work done by the spring as it stretches.
3. Explain how the electric field can be set up to keep the kinetic energy of the particle constant.

Answers:

1. The speed v of the particle can be determined using the formula for the radius of circular motion: r = mv/(qB). From the given information, v = qBr/m.

2. The work done by the spring (W) as it stretches from l to 2l is given by W = 0.5k((2l)^2 - l^2).

3. To keep the kinetic energy constant, an electric field E can be introduced such that it provides a force against the magnetic force. The condition qE = qvB must be maintained, implying E = vB.