JEE Advanced Numerical Examples

1. Magnetic field due to a long straight wire:

• Formula: $$B=\frac{{\mu }_{0}I}{2\pi r}$$
• Given values: (I = 10\text{ A}), ((x, y, z) = (3, 4, 0)\text{ m})
• Calculation: $$B=\frac{(4\pi \times {10}^{-7}\text{ Tm/A})(10\text{ A})}{2\pi (3\text{ m})}$$
• $$B=6.67\times {10}^{-7}\text{ T}$$

2. Magnetic field at the center of a circular loop:

• Formula: $$B=\frac{{\mu }_{0}I}{2R}$$
• Given values: (I = 2\text{ A}), (R = 5 \times 10^{-2} \text{ m})
• Calculation: $$B=\frac{(4\pi \times {10}^{-7}\text{ Tm/A})(2\text{ A})}{2(5\times {10}^{-2}\text{ m})}$$
• $$B=2.51\times {10}^{-5}\text{ T}$$

3. Magnetic field inside a solenoid:

• Formula: $$B={\mu }_{0}nI$$
• Given values: (n = \frac{1000 \text{ turns}}{0.2\text{ m}} = 5000 \text{ turns/m}), (I = 2\text{ A})
• Calculation: $$B=(4\pi \times {10}^{-7}\text{ Tm/A})(5000\text{ turns/m})(2\text{ A})$$
• $$B=0.126\text{ T}$$

4. Magnetic force on a moving proton:

• Formula: $$F=qvB\sin \theta$$
• Given values: (q = 1.6 \times 10^{-19}\text{ C}), (v = 10^6 \text{ m/s}), (B = 1\text{ T}), (\theta = 90^\circ)
• Calculation: $$F=(1.6\times {10}^{-19}\text{ C})({10}^6\text{ m/s})(1\text{ T})\sin {90}^{\circ }$$
• $$F=1.6\times {10}^{-13}\text{ N}$$

5. Frequency of revolution of an electron in a magnetic field:

• Formula: $$f=\frac{qvB}{2\pi m}$$
• Given values: (q = -1.6 \times 10^{-19}\text{ C}), (v = 10^6 \text{ m/s}), (B = 0.1\text{ T}), (m = 9.11 \times 10^{-31} \text{ kg})
• Calculation: $$f=\frac{(-1.6\times {10}^{-19}\text{ C})({10}^6\text{ m/s})(0.1\text{ T})}{2\pi (9.11\times {10}^{-31}\text{ kg})}$$
• $$f=2.81\times {10}^{12}\text{ Hz}$$

CBSE Board Exam Numerical Examples

1. Magnetic field due to a long straight wire:

• Formula: $$B=\frac{{\mu }_{0}I}{2\pi r}$$
• Given values: (I = 5\text{ A}), ((x, y, z) = (2, 3, 0)\text{ m})
• Calculation: $$B=\frac{(4\pi \times {10}^{-7}\text{ Tm/A})(5\text{ A})}{2\pi (2\text{ m})}$$
• $$B=5\times {10}^{-7}\text{ T}$$

2. Magnetic field at the center of a circular loop:

• Formula: $$B=\frac{{\mu }_{0}I}{2R}$$
• Given values: (I = 1\text{ A}), (R = 2 \times 10^{-2} \text{ m})
• Calculation: $$B=\frac{(4\pi \times {10}^{-7}\text{ Tm/A})(1\text{ A})}{2(2\times {10}^{-2}\text{ m})}$$
• $$B=6.28\times {10}^{-6}\text{ T}$$

3. Magnetic field inside a solenoid:

• Formula: $$B={\mu }_{0}nI$$
• Given values: (n = \frac{500 \text{ turns}}{0.1 \text{ m}} = 5000 \text{ turns/m}), (I = 1\text{ A})
• Calculation: $$B=(4\pi \times {10}^{-7}\text{ Tm/A})(5000\text{ turns/m})(1\text{ A})$$
• $$B=6.28\times {10}^{-4}\text{ T}$$

4. Magnetic force on a moving proton:

• Formula: $$F=qvB\sin \theta$$
• Given values: (q = 1.6 \times 10^{-19}\text{ C}), (v = 5 \times 10^5 \text{ m/s}), (B = 0.5\text{ T}), (\theta = 90^\circ)
• Calculation: $$F=(1.6\times {10}^{-19}\text{ C})(5\times {10}^5\text{ m/s})(0.5\text{ T})\sin {90}^{\circ }$$
• $$F=4\times {10}^{-14}\text{ N}$$

5. Frequency of revolution of an electron in a magnetic field:

• Formula: $$f=\frac{qvB}{2\pi m}$$
• Given values: (q = -1.6 \times 10^{-19}\text{ C}), (v = 10^6 \text{ m/s}), (B = 0.05\text{ T}), (m = 9.11 \times 10^{-31} \text{ kg})
• Calculation: $$f=\frac{(-1.6\times {10}^{-19}\text{ C})({10}^6\text{ m/s})(0.05\text{ T})}{2\pi (9.11\times {10}^{-31}\text{ kg})}$$
• $$f=8.79\times {10}^{11}\text{ Hz}$$