Magnetic Force on a Current Carrying Wire

This paragraph explains the concept of magnetic force acting on a wire carrying a current of 20 amps, which is 50 cm long, in a magnetic field of 4 tesla directed into the page. The right-hand rule is introduced to determine the direction of the force, which is found to be northward. The magnitude of the force is calculated using the formula F = I * L * B * sin(θ), where I is the current, L is the length of the wire, B is the magnetic field strength, and θ is the angle between the current and the magnetic field. Since the angle is 90 degrees, sin(θ) equals one, and the force is calculated to be 40 newtons. The explanation also includes an alternative method using the cross product in vector form to confirm the direction of the force.

The second paragraph delves into the concept of vector cross products, explaining how to determine the direction of the magnetic force using the i, j, and k unit vectors. It provides a brief introduction to the cross product and its rules, including the direction of the force when moving in a clockwise or counterclockwise manner. The paragraph also presents two problems to practice calculating cross products of different vector pairs. Finally, it applies the cross product concept to the magnetic force problem, emphasizing the importance of the order of vectors in the cross product formula and how it affects the direction of the resulting force.

This paragraph discusses two methods for determining the direction of the magnetic force acting on a current-carrying conductor. It starts by using the right-hand rule to find the direction when the current flows in the positive y-direction and the magnetic field in the positive x-direction, resulting in a force in the z-direction. The explanation then shifts to using the cross product of vectors i, j, and k to arrive at the same conclusion. The paragraph reinforces the understanding of the cross product and its application in physics, ensuring that the direction of the force is consistent with both methods.

The fourth paragraph focuses on calculating the force per unit length acting on a wire when a current of 15 amps flows south through a 2-meter wire with a magnetic field of 10 tesla directed out of the page. Using both the right-hand rule and the cross product method, the direction of the force is determined to be west or negative x-direction. The force per unit length is calculated by dividing the total force (F = I * L * B * sin(θ)) by the length of the wire, resulting in 150 newtons per meter. The paragraph also explains how the total force on a wire of different lengths can be calculated based on the force per unit length.

The final paragraph examines the variation of magnetic force with the angle between the current and the magnetic field. It presents several scenarios with different angles and calculates the magnetic force accordingly. The paragraph emphasizes that when the current and magnetic field are parallel, the force is minimal, and when they are perpendicular, the force is maximized. It illustrates this with examples, including a case where the angle is 60 degrees, resulting in a magnetic force of 2598 newtons. The summary highlights the importance of using the correct angle in calculations and the relationship between the angle and the magnitude of the magnetic force.